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Light plays an important role in determining plant architecture, which greatly influences crop yield. However, the precise mechanisms by which light signaling regulates bud outgrowth remain to be identified. Here, we show that light regulates bud outgrowth via both HY5 and brassinosteroid (BR)-dependent pathways in tomato. Inactivation of the red-light photoreceptor PHYB, or deficiencies in PHYB or the blue-light photoreceptor CRY1a, inhibits bud outgrowth and leads to decreased accumulation of HY5 protein and increased transcript level of BRANCHED1 ( BRC1 ), a central integrator of branching signals. HY5, functioning as a mobile systemic signal from leaves, promotes bud outgrowth by directly suppressing BRC1 transcript and activating the transcript of BR biosynthesis genes within the lateral buds in tomato. Furthermore, BRC1 prevents the accumulation of cytokinin (CK) and gibberellin (GA) by directly inhibiting the transcript of CK synthesis gene LOG4 , while increasing the transcript levels of CK and GA degradation genes ( CKX7 , GA2ox4 , and GA2ox5 ), leading to an arrest of bud outgrowth. Moreover, bud outgrowth occurs predominantly in the day due to the suppression of BRC1 transcript by HY5. These findings demonstrate that light-inducible HY5 acts as a systemic signaling factor in fine-tuning the bud outgrowth of tomato.

Phytosulfokine (PSK) is a danger-associated molecular pattern recognized by PHYTOSULFOKINE RECEPTOR 1 (PSKR1) and initiates intercellular signaling to coordinate different physiological processes, especially in the defense response to the necrotrophic fungus Botrytis cinerea. The activity of peptide receptors is largely influenced by different posttranslational modifications, which determine intercellular peptide signal outputs. To date, the posttranslational modification to PHYTOSULFOKINE RECEPTOR 1 (PSKR1) remains largely unknown. Here, we show that tomato (Solanum lycopersicum) PSKR1 is regulated by the ubiquitin/proteasome degradation pathway. Using multiple protein–protein interactions and ubiquitylation analyses, we identified that plant U-box E3 ligases PUB12 and PUB13 interacted with PSKR1, among which PUB13 caused PSKR1 ubiquitylation at Lys-748 and Lys-905 sites to control PSKR1 abundance. However, this posttranslational modification was attenuated upon addition of PSK. Moreover, the disease symptoms observed in PUB13 knock-down and overexpression lines demonstrated that PUB13 significantly suppressed the PSK-initiated defense response. This highlights an important regulatory function for the turnover of a peptide receptor by E3 ligase-mediated ubiquitylation in the plant defense response.

Phytosulfokine (PSK) is a plant pentapeptide hormone that fulfills a wide range of functions. Although PSK has frequently been reported to function in the inverse regulation of growth and defense in response to (hemi)biotrophic pathogens, the mechanisms involved remain largely unknown. Using the tomato (Solanum lycopersicum) and Pseudomonas syringae pv. tomato (Pst) DC3000 pathogen system, we present compelling evidence that the PSK receptor PSKR1 interacts with the calcium-dependent protein kinase CPK28, which in turn phosphorylates the key enzyme of nitrogen assimilation glutamine synthetase GS2 at two sites (Serine-334 and Serine-360). GS2 phosphorylation at S334 specifically regulates plant defense, whereas S360 regulates growth, uncoupling the PSK-induced effects on defense responses and growth regulation. The discovery of these sites will inform breeding strategies designed to optimize the growth-defense balance in a compatible manner.

The ubiquitous lipid-derived molecules N-acylethanolamines (NAEs) have multiple immune functions in mammals, but their roles and mechanisms in plant defense response during changing environment remain largely unclear. Here, we found that exogenous NAE18:0 and NAE18:2 promoted defense against the necrotrophic pathogen Botrytis cinerea but suppressed defense to the hemi-biotrophic pathogen Pseudomonas syringae pv. tomato (Pst) DC3000 in tomato. The knocking-down and overexpression function analysis of the pathogen-responsive NAE synthetic gene PHOSPHOLIPASE Dγ (PLDγ) and hydrolytic gene FATTY ACID AMID HYDROLASE 1 (FAAH1) revealed that the NAE pathway is crucial for plant defense response. Using exogenous applications and SA-abolished NahG plants, we unveiled the antagonistic relationship between NAE and SA in plant defense response. Elevated CO2 and temperature significantly changed the NAE pathway in response to pathogens, while inhibition of the NAE pathway led to the alternation of environment-mediated defense variations against Pst DC3000 in tomato, indicating that NAE pathway is associated with plant defense variations in response to elevated CO2 and temperature. The results herein reveal a new function of NAE in plant defense, and its involvement in environment-mediated defense variation in tomato. These findings shed light on the NAE-based plant defense, which may have relevance to crop disease management in future changing climate.

Herbivory severely affects plant growth, posing a threat to crop production. Calcium ion (Ca

High temperatures are a major threat to plant growth and development, leading to yield losses in crops. Calcium-dependent protein kinases (CPKs) act as critical components of Ca2+ sensing in plants that transduce rapid stress-induced responses to multiple environmental stimuli. However, the role of CPKs in plant thermotolerance and their mechanisms of action remain poorly understood. To address this issue, tomato (Solanum lycopersicum) cpk28 mutants were generated using a CRISPR-Cas9 gene-editing approach. The responses of mutant and wild-type plants to normal (25°C) and high temperatures (45°C) were documented. Thermotolerance was significantly decreased in the cpk28 mutants, which showed increased heat stress-induced accumulation of reactive oxygen species (ROS) and levels of protein oxidation, together with decreased activities of ascorbate peroxidase (APX) and other antioxidant enzymes. The redox status of ascorbate and glutathione were also modified. Using a yeast two-hybrid library screen and protein interaction assays, we provide evidence that CPK28 directly interacts with cytosolic APX2. Mutations in APX2 rendered plants more sensitive to high temperatures, whereas the addition of exogenous reduced ascorbate (AsA) rescued the thermotolerance phenotype of the cpk28 mutants. Moreover, protein phosphorylation analysis demonstrated that CPK28 phosphorylates the APX2 protein at Thr-59 and Thr-164. This process is suggested to be responsive to Ca2+ stimuli and may be required for CPK28-mediated thermotolerance. Taken together, these results demonstrate that CPK28 targets APX2, thus improving thermotolerance. This study suggests that CPK28 is an attractive target for the development of improved crop cultivars that are better adapted to heat stress in a changing climate.

We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.

To investigate the multi-scale structural changes and digestibility of parboiled rice, the side chain distribution, helical structure, short/long-range ordered structure, and lamellar structure were systematically characterized and an in vivo postprandial blood glucose test was applied. The results indicate that parboiling has little effect on the side chain distribution, double helix content and helical structure order of parboiled rice. The crystal type of rice starch changed from type A to A + V or B + V after parboiling and the relative crystallinity decreased from 30.45 % to a minimum of 6.87 %. The in vivo study also indicated that parboiling significantly reduces the glycaemic index of rice to medium level. Our work is the first to focus on the parboiling conditions, multi-scale structural changes and in vivo digestibility of parboiled rice, which might provide guidance for the design of less digestible parboiled rice in the future.

Atmospheric CO2 concentrations exert a strong influence on the susceptibility of plants to pathogens. However, the mechanisms involved in the CO2 -dependent regulation of pathogen resistance are largely unknown. Here we show that the expression of tomato (Solanum lycopersicum) β-CARBONIC ANHYDRASE 3 (βCA3) is induced by the virulent pathogen Pseudomonas syringae pv. tomato DC3000. The role of βCA3 in the high CO2 -mediated response in tomato and two other Solanaceae crops is distinct from that in Arabidopsis thaliana. Using βCA3 knock-out and over-expression plants, we demonstrate that βCA3 plays a positive role in the activation of basal immunity, particularly under high CO2 . βCA3 is transcriptionally activated by the transcription factor NAC43 and is also post-translationally regulated by the receptor-like kinase GRACE1. The βCA3 pathway of basal immunity is independent on stomatal- and salicylic-acid-dependent regulation. Global transcriptome analysis and cell wall metabolite measurement implicate cell wall metabolism/integrity in βCA3-mediated basal immunity under both CO2 conditions. These data not only highlight the importance of βCA3 in plant basal immunity under high CO2 in a well-studied susceptible crop-pathogen system, but they also point to new targets for disease management strategies in a changing climate.

We give a complete characterization of Schatten class Hankel operators H f H_f acting on weighted Segal-Bargmann spaces F 2 ( φ ) F^2(\varphi ) using the notion of integral distance to analytic functions in C n \mathbb {C}^n and Hörmander’s ∂ ¯ \bar \partial -theory. Using our characterization, for f ∈ L ∞ f\in L^\infty and 1 > p > ∞ 1>p>\infty , we prove that H f H_f is in the Schatten class S p S_p if and only if H f ¯ ∈ S p H_{\bar {f}}\in S_p , which was previously known only for the Hilbert-Schmidt class S 2 S_2 of the standard Segal-Bargmann space F 2 ( φ ) F^2(\varphi ) with φ ( z ) = α | z | 2 \varphi (z) = \alpha |z|^2 .

Recently the authors characterized the Fredholmn properties of Toeplitz operators on weighted Fock spaces when the Laplacian of the weight function is bounded below and above. In the present work the authors extend their characterization to doubling Fock spaces with a subharmonic weight whose Laplacian is a doubling measure. The geometry induced by the Bergman metric for doubling Fock spaces is much more complicated than that of the Euclidean metric used in all the previous cases to study Fredholmness, which leads to considerably more involved calculations.

Low light intensities affect the outbreak of plant diseases. However, the underlying molecular mechanisms remain poorly understood. High-performance liquid chromatography analysis of tomato (Solanum lycopersicum) revealed that apoplastic glucose (Glc) levels decreased in response to low light. Conversely, low-light-induced susceptibility to Pseudomonas syringae pv tomato (Pst) DC3000 was significantly alleviated by exogenous Glc treatment. Using cell-based biolayer interferometry assays, we found that Glc specifically binds to the tomato regulator of G protein signaling 1 (RGS1). Laser scanning confocal microscopy imaging revealed that Glc triggers RGS1 endocytosis, which influences the uncoupling of the RGS1-Gα (GPA1) and GPA1-Gβ (SlGB1) proteins, in a dose- and duration-dependent manner. Analysis of G protein single and double mutants revealed that RGS1 negatively regulates disease resistance under low light and is required for Glc-enhanced defense. Downstream of RGS1-Glc binding, GPA1 negatively mediates the light-intensity-regulated defense, whereas SlGB1 positively regulates this process. These results reveal a novel light-intensity-responsive defense system that is mediated by a Glc-RGS1-G protein signaling pathway. This information will be critical for future investigations of how plant cells sense extracellular sugars and adjust defense under different environments, as well as for genetic engineering approaches to improve stress resilience.

Suppose D is a bounded strongly pseudoconvex domain in $${{\mathbb {C}}}^n$$ with smooth boundary, and let $$\rho $$ be its defining function. For $$1< p-1$$ , we show that the weighted Bergman projection $$P_\alpha $$ is bounded on $$L^p(D, |\rho |^\alpha dV)$$ . With non-isotropic estimates for $$\overline{\partial }$$ and Stein’s theorem on non-tangential maximal operators, we prove that bounded holomorphic functions are dense in the weighted Bergman space $$A^p(D, |\rho |^\alpha dV)$$ , and hence Hankel operators can be well defined on these spaces. For all $$1

In this paper, we characterize the mapping properties of Hankel operators $$H_{g}$$ and $$ H_{\overline{g}}$$ associated to some restricted function g on the complex space $$\mathbf{C}^n$$ . We, in particular, describe the boundedness and compactness of operators $$H_{g}$$ and $$ H_{\overline{g}}$$ acting between Fock spaces in terms of Berezin transforms of their inducing function g. Our results extend a recent work of Z. Hu and E. Wang and fills the remaining gap when the largest Fock spaces are taken into account. And for $$1 \le s, p \le \infty $$ , we also obtain the characterization on $$IMO^{s,p}$$ , the space of functions satisfying an integral condition for the mean oscillation, via Berezin transform.

We characterize Fredholmness of Toeplitz operators acting on generalized Fock spaces of the n-dimensional complex space for symbols in the space of vanishing mean oscillation VMO. Our results extend the recent characterizations for Toeplitz operators on standard weighted Fock spaces to the setting of generalized weight functions and also allow for unbounded symbols in VMO for the first time. Another novelty is the treatment of small exponents 0 < p < 1, which to our knowledge has not been seen previously in the study of the Fredholm properties of Toeplitz operators on any function spaces. We accomplish this by describing the dual of the generalized Fock spaces with small exponents.

Fruits are excellent sources of essential vitamins and health-boosting minerals. Recently, regulation of fruit ripening by both internal and external cues for the improvement of fruit quality and shelf life has received considerable attention. Rosmarinic acid (RA) is a kind of natural plant-derived polyphenol, widely used in the drug therapy and food industry due to its distinct physiological functions. However, the role of RA in plant growth and development, especially at the postharvest period of fruits, remains largely unknown. Here, we demonstrated that postharvest RA treatment delayed the ripening in tomato fruits. Exogenous application of RA decreased ripening-associated ethylene production and inhibited the fruit color change from green to red based on the decline in lycopene accumulation. We also found that the degradation of sucrose and malic acid during ripening was significantly suppressed in RA-treated tomato fruits. The results of metabolite profiling showed that RA application promoted the accumulation of multiple amino acids in tomato fruits, such as aspartic acid, serine, tyrosine, and proline. Meanwhile, RA application also strengthened the antioxidant system by increasing both the activity of antioxidant enzymes and the contents of reduced forms of antioxidants. These findings not only unveiled a novel function of RA in fruit ripening, but also indicated an attractive strategy to manage and improve shelf life, flavor, and sensory evolution of tomato fruits.

In this paper, we focus on the weighted Bergman spaces $A_{\varphi}^{p}$ in $\mathbb{D}$ with $\varphi\in\mathcal{W}_{0}$. We first give characterizations of those finite positive Borel measures $\mu$ in $\mathbb{D}$ such that the embedding $A_{\varphi}^{p}\subset L_{\mu}^{q}$ is bounded or compact for $0, Comment: 26 pages

In this note, we discuss the Bergman projection P and Toeplitz operators $$T_{\mu }$$ with positive measure symbol $$\mu $$ between $$F^p_{\Psi }(\mathbb {C}^n)$$ and $$F^q_{\Psi }(\mathbb {C}^n)$$ for $$1\le p, q\le \infty $$ . We first show that P is a bounded projection from $$L^p_{\Psi }$$ onto $$F^p_{\Psi }$$ when $$1\le p\le \infty $$ , and then apply it to obtain results on the complex interpolation and the duality of the Fock-type spaces. Furthermore, we obtain the equivalent conditions for the boundedness and compactness of $$T_{\mu }$$ in terms of the averaging function and the Berezin transform, which extend the main results about Toeplitz operators of Seip and Youssfi (J Geom Anal 23:170–201, 2013).

In this paper we introduce a kind of Bergman space A φ p on the unit disk D with exponential weights, which cover those defined by Borichev et al. (2007) [6] . We obtain upper and lower bound estimates on the Bergman kernel. As an application, we discuss the Bergman projection and duality.

Given some regular weight $$\omega $$ on the unit disk $$\mathbb {D}$$, let $$L^p_\omega $$ be the space of all Lebesgue measurable functions on $$\mathbb {D}$$ for which $$\begin{aligned} \Vert f\Vert _{L^p_\omega }=\left( \int _{\mathbb {D}} |f(z)|^p \omega (z)\mathrm{d}A(z)\right) ^{\frac{1}{p}}

Nitrogen (N) influences a myriad of physiological processes while its effects on plant defences and the underlying mechanisms are largely unknown. Here, the interaction between tomato and pathogens was examined under four N regimes (sole NO3 - or mixed NO3 - /NH4 + of total 1 and 7 mM N, denoting low and high N regimes, respectively) followed by inoculation with two bacterial pathogens, Pseudomonas syringae and Ralstonia solanacearum. Tomato immunity against both pathogens was generally higher under low N as well as NO3 - as the sole N source. The disease susceptibility was reduced by silencing N metabolism genes such as NR, NiR and Fd-GOGAT, while increased in NiR1-overexpressed plants. Further studies demonstrated that the N-modulated defence was dependent on the salicylic acid (SA) defence pathway. Low N as well as the silencing of N metabolism genes increased the SA levels and transcripts of its maker genes, and low N-enhanced defence was blocked in NahG transgenic tomato plants that do not accumulate SA, while exogenous SA application attenuated the susceptibility of OE-NiR1. The study provides insights into the mechanisms of how nitrogen fertilization and metabolism affect plant immunity in tomato, which might be useful for designing effective agronomic strategies for the management of N supply.

With global climate change, plants are frequently being exposed to various stresses, such as pathogen attack, drought, and extreme temperatures. Transcription factors (TFs) play crucial roles in numerous plant biological processes; however, the functions of many tomato (Solanum lycopersicum L.) TFs that regulate plant responses to multiple stresses are largely unknown. Here, using an RNA-seq approach, we identified SlNAP1, a NAC TF-encoding gene, which was strongly induced by various stresses. By generating SlNAP1 transgenic lines and evaluating their responses to biotic and abiotic stresses in tomato, we found that SlNAP1-overexpressing plants showed significantly enhanced defense against two widespread bacterial diseases, leaf speck disease, caused by Pseudomonas syringae pv. tomato (Pst) DC3000, and root-borne bacterial wilt disease, caused by Ralstonia solanacearum. In addition, SlNAP1 overexpression dramatically improved drought tolerance in tomato. Although the SlNAP1-overexpressing plants were shorter than the wild-type plants during the early vegetative stage, eventually, their fruit yield increased by 10.7%. Analysis of different hormone contents revealed a reduced level of physiologically active gibberellins (GAs) and an increased level of salicylic acid (SA) and abscisic acid (ABA) in the SlNAP1-overexpressing plants. Moreover, EMSAs and ChIP-qPCR assays showed that SlNAP1 directly activated the transcription of multiple genes involved in GA deactivation and both SA and ABA biosynthesis. Our findings reveal that SlNAP1 is a positive regulator of the tomato defense response against multiple stresses and thus may be a potential breeding target for improving crop yield and stress resistance.

Atmospheric CO

Plant peptides secreted as signal molecular to trigger cell-to-cell signaling are indispensable for plant growth and defense processes. Preciously, it is regraded some plant peptides function in plant growth and development, whereas others regulate defense response in plant-microbe interactions. However, this prejudice is got rid due to more and more evidence showed growth-related plant peptides also exhibit bifunctional roles in plant defense response against different microbial pathogens. Here we provide a mini-review of reported types of plant peptides, including their basic information, reported receptor ligands, and especially direct or indirect roles in plant immune responses.

For $0, Comment: 23 Pages

Phytosulfokine (PSK) is a disulfated pentapeptide that is an important signaling molecule. Although it has recently been implicated in plant defenses to pathogen infection, the mechanisms involved remain poorly understood. Using surface plasmon resonance and gene silencing approaches, we showed that the tomato (Solanum lycopersicum) PSK receptor PSKR1, rather than PSKR2, functioned as the major PSK receptor in immune responses. Silencing of PSK signaling genes rendered tomato more susceptible to infection by the economically important necrotrophic pathogen Botrytis cinerea Analysis of tomato mutants defective in either defense hormone biosynthesis or signaling demonstrated that PSK-induced immunity required auxin biosynthesis and associated defense pathways. Here, using aequorin-expressing tomato plants, we provide evidence that PSK perception by tomato PSKR1 elevated cytosolic [Ca2+], leading to auxin-dependent immune responses via enhanced binding activity between calmodulins and the auxin biosynthetic YUCs. Thus, our data demonstrate that PSK acts as a damage-associated molecular pattern and is perceived mainly by PSKR1, which increases cytosolic [Ca2+] and activates auxin-mediated pathways that enhance immunity of tomato plants to B. cinerea.

Given f in the Fock space Fα∞ , for all possible 1≤p,q

Let $$F^{2}_\varphi $$ be the generalized Fock space defined as $$\begin{aligned} F^2_\varphi =\left\{ f {\text { holomorphic in }} {{\mathbf {C}}^n}: \Vert f\Vert _{2, \varphi }= \left( \int _{{{{\mathbf {C}}^n}}}\left| f(z) e^{-\varphi (z)}\right| ^{2} dv(z)\right) ^\frac{1}{2}

Given a bounded strongly pseudoconvex domain D in with smooth boundary, we characterize -Bergman Carleson measures for , , and . As an application, we show that the Bergman space version of the balayage of a Bergman Carleson measure on D belongs to BMO in the Kobayashi metric.

This paper is a timely survey on generalized Fock spaces and operators acting on them. It contains the definition of Fock spaces with various weights, the precise estimates on the Bergman kernel, the equivalent norms and the Carleson measures. Also, some recent progress on the study of certain operators on Fock spaces is introduced, which includes composition operators, extended Cesaro operators, Toeplitz operators, Hankel operators, and those in the closed algebra generated by weakly localized operators.

Tropospheric CO2 concentrations were remarkably increasing, especially since the Industrial Revolution. The CO2 fertilization technology was increasingly used in greenhouse agriculture cultivation because of its benefit to crop quality and yield. But, as a consequence of elevated CO2, the plant-pathogen interactions in natural or agricultural ecosystems have large potential to be affected. So far, the effects of elevated CO2 on plant defense against pathogen are complicated and the underlying mechanism remained poorly understood. Here, using tomato plants, we found that elevated CO2 significantly suppressed the plant defense against necrotrophic pathogen Botrytis cinerea, which is accompanied by the disturbed homeostasis between defense-related salicylic acid- and jasmonic acid- (JA-) signaling. But, exogenous application of bacterial secreta N-decanoyl-homoserine lactone (DHL) drastically rescued B. cinerea disease susceptibility under elevated CO2 condition. Moreover, JA biosynthesis mutant spr2 and JA signaling gene-silenced plants blocked DHL-induced plant defense under elevated CO2 condition, which suggested JA signaling was indispensable to the alleviated effect of DHL on plant susceptibility to B. cinerea under elevated CO2 condition. Overall, this information will be benefit to manipulate DHL as an attractive disease management strategy in agriculture cultivation under changing CO2 conditions.

Plants have evolved two tiers of immune receptors to detect infections: cell surface-resident pattern recognition receptors (PRRs) that sense microbial signatures and intracellular nucleotide binding domain leucine-rich repeat (NLR) proteins that recognize pathogen effectors. How PRRs and NLRs interconnect and activate the specific and overlapping plant immune responses remains elusive. A genetic screen for components controlling plant immunity identified ANXUR1 (ANX1), a malectin-like domain-containing receptor-like kinase, together with its homolog ANX2, as important negative regulators of both PRR- and NLR-mediated immunity in Arabidopsis thaliana ANX1 constitutively associates with the bacterial flagellin receptor FLAGELLIN-SENSING2 (FLS2) and its coreceptor BRI1-ASSOCIATED RECEPTOR KINASE1 (BAK1). Perception of flagellin by FLS2 promotes ANX1 association with BAK1, thereby interfering with FLS2-BAK1 complex formation to attenuate PRR signaling. In addition, ANX1 complexes with the NLR proteins RESISTANT TO PSEUDOMONAS SYRINGAE2 (RPS2) and RESISTANCE TO P. SYRINGAE PV MACULICOLA1. ANX1 promotes RPS2 degradation and attenuates RPS2-mediated cell death. Surprisingly, a mutation that affects ANX1 function in plant immunity does not disrupt its function in controlling pollen tube growth during fertilization. Our study thus reveals a molecular link between PRR and NLR protein complexes that both associate with cell surface-resident ANX1 and uncovers uncoupled functions of ANX1 and ANX2 during plant immunity and sexual reproduction.

In this paper, we show that, on the generalized Fock space \({F^p(\varphi)}\) with \({1 < p < \infty}\) , the essential norm of a noncompact Toeplitz operator \({T_\mu}\) with \({|\mu|}\) being a Fock–Carleson measure equals its distance to the set of compact Toeplitz operators. Moreover, the distance is realized by infinitely many compact Toeplitz operators. Our approach is also available on the Bergman space setting.

N-decanoyl-homoserine lactone activates plant systemic resistance against Botrytis cinerea in tomato plants, which is largely dependent on jasmonic acid biosynthesis and signal transduction pathways. Rhizosphere bacteria secrete N-acylated-homoserine lactones (AHLs), a type of specialized quorum-sensing signal molecule, to coordinate their population density during communication with their eukaryotic hosts. AHLs behave as low molecular weight ligands that are sensed by plants and promote the host’s resistance against foliar pathogens. In this study, we report on N-decanoyl-homoserine lactone (DHL), which is a type of AHL that induces systemic immunity in tomato plants and protects the host organism against the necrotrophic fungus Botrytis cinerea. Upon DHL treatment, tomato endogenous jasmonic acid (JA) biosynthesis (rather than salicylic acid biosynthesis) and signal transduction were significantly activated. Strikingly, the DHL-induced systemic resistance against B. cinerea was blocked in the tomato JA biosynthesis mutant spr2 and JA signaling gene-silenced plants. Our findings highlight the role of DHL in systemic resistance against economically important necrotrophic pathogens and suggest that DHL-induced immunity against B. cinerea is largely dependent on the JA signaling pathway. Manipulation of DHL-induced resistance is an attractive disease management strategy that could potentially be used to enhance disease resistance in diverse plant species.

Let $F^{p}(\phi)$ be the weighted Fock space on the complex plane $\mathbb{C}$, where $\phi$ is subharmonic with $\Delta \phi \, dA$ a doubling measure. In this paper, we characterize the positive Borel measure $\mu$ on $\mathbb{C}$ for which the induced Toeplitz operator $T_\mu$ is bounded (or compact) from one weighted Fock space $F^{p}(\phi)$ to another $F^{q}(\phi)$ for $0 \lt p, q \lt \infty$.

Given \({\varphi\in \verb"C"^2(\textbf{C}^n)}\) satisfying \({dd^{c}\varphi\simeq \omega_0}\), 0 < p < ∞, let \({F^p(\varphi)}\) be the generalized Fock space of all holomorphic functions f on \({{\mathbf C}^n}\) for which the Fock norm $$\|f\|_{p, \varphi}=\left(\,\int_{{\mathbf C}^n} \left|f(z)\right|^{p}e^ {-p\varphi(z)}dv(z)\right)^{\frac{1}{p}} < \infty. $$ While \({\varphi(z)=\frac{1}{2}|z|^2}\), \({F^{p}(\varphi)}\) is the classical Fock space Fp. In this paper, for all possible 0 < p,q < ∞ we characterize those positive Borel measures μ on \({{\mathbf C}^n}\) for which the induced Toeplitz operators Tμ are bounded (or compact) from one generalized Fock spaces \({F^p(\varphi)}\) to another \({F^q(\varphi)}\). With symbols \({g\in BMO}\), we obtain Zorborska’s criterion for boundedness (or compactness) of Toeplitz operators Tg on Fp, our work extends the known results on F2. Toeplitz operators on p-th Fock space with 0 < p < 1 have not been studied before, even in the simplest case that \({\varphi(z)=\frac{1}{2}|z|^2}\). Our analysis shows a significant difference between Bergman spaces and Fock spaces.

National Natural Science Foundation of China [11101139, 11271124]; Natural Science Foundation of Zhejiang Province [Y6090036, Y6100219]; Foundation of Creative Group in Universities of Zhejiang Province [T200924]