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For the Hardy-Littlewood maximal and Calder\'on-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak Orlicz-Morrey spaces. To do this we show the weak-weak modular inequality. The Orlicz-Morrey space and its weak version contain weighted Orlicz, Morrey and Lebesgue spaces and their weak versions as special cases. Then we also get the boundedness for these function spaces as corollaries., Comment: 23 pages. arXiv admin note: text overlap with arXiv:2107.10553, arXiv:2007.00468

background Intracranial hypotension due to cerebrospinal fluid (CSF) leak is often associated with secondary chronic subdural hematoma (CSDH). Although epidural blood patch (EBP) treatment for the CSF leak site has been reported to result in spontaneous regression of the CSDH in most cases, it is still debatable whether blocking CSF leak first in the patients with intracranial hematoma is always safe. Case Description A 72-year-old woman presented with orthostatic headache after a head injury and was diagnosed with intracranial hypotension. Computed tomography myelography and radioisotope cisternography failed to reveal the CSF leak point. The overflow leak test, a novel diagnostic method for intracranial hypotension, revealed a leakage at the cervical spine. Bilateral CSDHs were also observed by a computed tomography scan of the head. We performed EBP at the cervical spine and anticipated subsequent regression of the CSDH by normalizing intrathecal pressure. However, the patient became delirious the morning after EBP, and an emergency burr hole trepanation was performed. The patient's consciousness fully recovered, and her orthostatic headache improved as well. Conclusions This case presentation demonstrated that in the case of intracranial hypotension with secondary CSDH, performing EBP and waiting for subsequent spontaneous regression of CSDH are not necessarily safe. Immediate burr hole trepanation should be prepared for the subsequent rapid symptomatic change of the CSDH after EBP.

We consider generalized weak Morrey spaces with variable growth condition on spaces of homogeneous type and characterize the pointwise multipliers from a generalized weak Morrey space to another one. The set of all pointwise multipliers from a weak Lebesgue space to another one is also a weak Lebesgue space. However, we point out that the weak Morrey spaces do not always have this property just as the Morrey spaces not always.

We prove that block spaces defined on ℝ n {\mathbb{R}^{n}} with an arbitrary Radon measure, which are known to be the preduals of Morrey spaces, are closed under the first and the second complex interpolation method. The proof of our main theorem uses the duality theorem in the complex interpolation method, the complex interpolation of certain closed subspaces of Morrey spaces, a characterization of the preduals of block spaces, and some formulas related to the Calderón product.

We prove that the Riesz potential operator $$I_\alpha $$ of order $$\alpha $$ embeds from Musielak–Orlicz–Morrey spaces $$L^{\Phi ,\nu }(\mathbf{R}^N)$$ of the double phase functionals $$\Phi (x,t)= t^{p} + (b(x) t)^{q}$$ to Campanato–Morrey spaces, where $$1

We consider the commutators $[b,T]$ and $[b,I_{\rho}]$ on Orlicz-Morrey spaces, where $T$ is a Calder\'on-Zygmund operator, $I_{\rho}$ is a generalized fractional integral operator and $b$ is a function in generalized Campanato spaces. We give a necessary and sufficient condition for the boundedness of the commutators on Orlicz-Morrey spaces. To do this we prove the boundedness of generalized fractional maximal operators on Orlicz-Morrey spaces. Moreover, we introduce Orlicz-Campanato spaces and establish their relations to Orlicz-Morrey spaces., Comment: 45 pages. arXiv admin note: text overlap with arXiv:1812.09148

A hybrid operating room(Hybrid OR), where operative equipment and flat panel angiography are both available, is becoming common for complex cerebrovascular surgery. However, the current Hybrid OR remains suboptimal as it is not cost-effective and contains uncomfortable operating beds, and a single-plane flat panel. Therefore, we introduced a novel Hybrid OR system, which has a biplane flat panel detector and three mutually exchangeable tailor-made operating beds. In this article, we report our preliminary experience of this novel Hybrid OR, focusing on improved cost-effectiveness by the availability of diagnostic angiography and standard endovascular surgery, optimal selection of three different types of operating beds, and procedural workflow in individual hybrid cerebrovascular surgery.

Background Cerebrospinal fluid (CSF) hypovolemia is usually treated via an epidural blood patch (EBP). Accurate placement of the EBP at the site of CSF leakage is required for successful treatment of CSF hypovolemia. The thoracolumbar spine is evidently a common site of leakage, but because rates of detection of the leakage site via conventional imaging have historically not been high, there may be other common leakage sites. In this study, CSF leakage sites were identified via a combination of conventional imaging, a new method called the overflow leak test, and patient interviews. Methods CSF leakage sites were identified using computed tomography myelography, radioisotope cisternography, and the overflow leak test in 14 patients with CSF hypovolemia. The patients were also asked about their history with regard to potential trauma. EBP was performed, and the accuracy of leakage site identification was assessed. Results Conventional imaging identified a leakage site in 7 of 14 patients, and in most cases it was in the lumbar spine. In the remaining 7 cases, the overflow leak test and ascertaining a history of trauma facilitated identification of the cervical spine as a leakage site. The site of the EBP was the cervical spine in 10 patients and the lumbar spine in 4 patients. Complete recovery was observed in 13 of 14 patients. Conclusions The cervical spine was a common leakage site in this study. Leakage in the cervical spine was undetectable via conventional imaging, suggesting that many cases of cervical spine leakage may remain undetected.

In 1978 Uchiyama gave a proof of the characterization of $\mathrm{CMO}(\mathbb{R}^n)$ which is the closure of $C^{\infty}_{\rm comp}(\mathbb{R}^n)$ in $\mathrm{BMO}(\mathbb{R}^n)$. We extend the characterization to the closure of $C^{\infty}_{\rm comp}(\mathbb{R}^n)$ in the Campanato space with variable growth condition. As an application we characterize compact commutators $[b,T]$ and $[b,I_{\alpha}]$ on Morrey spaces with variable growth condition, where $T$ is the Calderón–Zygmund singular integral operator, $I_{\alpha}$ is the fractional integral operator and $b$ is a function in the Campanato space with variable growth condition.

Astroblastoma is a rare, supratentorial glial tumor, occurring predominantly in children and young adults. However, treatment strategies have not yet been established for this rare disease.A 6-year-old boy presented with headache and nausea. CT and MRI revealed a left frontal mass lesion with slight edema and macrocalcifications. Gross tumor resection was performed. Histological examination found neoplastic cells with astroblastic characteristics, and a striking perivascular array of pseudorosettes. The final diagnosis was high-grade astroblastoma. MRI 13 months after surgery suggested local recurrence, and an enlargement was found 3 months later. Stereotactic radiotherapy(SRT)was performed. MRI after SRT showed enhanced cyst formation around the tumor bed, suggesting tumor recurrence. However,Astroblastoma is rare, therefore, no optimal management is known. SRT may be effective to treat recurrent astroblastomas.

For the multiple Fourier series of the periodization of some radial functions on $\mathbb{R}^d$, we investigate the behavior of the spherical partial sum. We show the Gibbs-Wilbraham phenomenon, the Pinsky phenomenon and the third phenomenon for the multiple Fourier series, involving the convergence properties of them. The third phenomenon is closely related to the lattice point problems, which is a classical theme of the analytic number theory. We also prove that, for the case of two or three dimension, the convergence problem on the Fourier series is equivalent to the lattice point problems in a sense. In particular, the convergence problem at the origin in two dimension is equivalent to Hardy's conjecture on Gauss's circle problem., 64 pages, 27 figures

In the present paper, we will characterize the boundedness of the generalized fractional integral operators I? and the generalized fractional maximal operators M? on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators M? and I? on generalized Orlicz–Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators M? and I? on generalized Orlicz–Morrey spaces. © 2018, Springer Nature Switzerland AG., Ministry of Education and Science of the Russian Federation: 15H03621, 02. FEF.A4.18.019, EIF-BGM-4-RFTF-1/2017-21/01/1 Japan Society for the Promotion of Science: 16K05209, The research of F. Deringoz was partially supported by the Grant of Ahi Evran University Scientific Research Project (FEF.A4.18.019). The research of V. Guliyev was partially supported by the Grant of 1st Azerbaijan–Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/2017-21/01/1) and by the Ministry of Education and Science of the Russian Federation (the Agreement No. 02.a03.21.0008). Eiichi Nakai was supported by Grant-in-Aid for Scientific Research (B), No. 15H03621, Japan Society for the Promotion of Science. Yoshihiro Sawano was supported by Grant-in-Aid for Scientific Research (C) (16K05209), the Japan Society for the Promotion of Science and by Peoples Friendship University of Russia. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We consider the commutators $[b,T]$ and $[b,I_{\rho}]$, where $T$ is a Calderon-Zygmund operator, $I_{\rho}$ is a generalized fractional integral operator and $b$ is a function in Campanato spaces with variable growth condition. It is known that these commutators are bounded on generalized Morrey spaces with variable growth condition. In this paper we discuss the compactness of these commutators.

We establish the boundedness and weak boundedness of the maximal operator and generalized fractional integral operators on generalized Morrey spaces over metric measure spaces (X,d,I¼) without the assumption of the growth condition on I¼. The results are generalization and improvement of some known results. We also give the vector†valued boundedness. Moreover we prove the independence of the choice of the parameter in the definition of generalized Morrey spaces by using the geometrically doubling condition in the sense of HytA¶nen.

We use the Morrey norm estimate for the imaginary power of the Laplacian to prove an interpolation inequality for the fractional power of the Laplacian on Morrey spaces. We then prove a Hardy-type inequality and use it together with the interpolation inequality to obtain a Heisenberg-type inequality in Morrey spaces.

In this paper, the size of the embedding constant from weak Morrey spaces into Morrey spaces is specified. As a by-product, the difference between weak Morrey spaces and Morrey spaces is clarified.

We consider the commutators [b, T] and $$[b,I_{\rho }]$$ , where T is a Calderon–Zygmund operator, $$I_{\rho }$$ is a generalized fractional integral operator and b is a function in generalized Campanato spaces with variable growth condition. We give necessary and sufficient conditions for the boundedness of the commutator on generalized Morrey spaces with variable growth condition.

We investigate the boundedness of singular and fractional integral operators on generalized Hardy spaces defined on spaces of homogeneous type, which are preduals of Campanato spaces with variable growth condition. To do this we introduce molecules with variable growth condition. Our results are new even for ℝ n case.

We give new viewpoints of Campanato spaces with variable growth condition for applications to the Navier-Stokes equation. Namely, we formulate a blowup criteria along maximum points of the 3D-Navier-Stokes flow in terms of stationary Euler flows and show that the properties of Campanato spaces with variable growth condition are very useful for this formulation, since variable growth condition can control the continuity and integrability of functions on the neighborhood at each point. Our criterion is different from the Beale-Kato-Majda type and Constantin-Fefferman type criterion. If geometric behavior of the velocity vector field near the maximum point has a kind of stationary Euler flow configuration up to a possible blowup time, then the solution can be extended to be the strong solution beyond the possible blowup time. As another application we also mention the Cauchy problem for the Navier-Stokes equation.

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying that there exists a constant $p_0\in(0,p_-)$, where $p_-:=\mathop{\mathrm {ess\,inf}}_{x\in \mathbb R^n}p(x)$, such that the Hardy-Littlewood maximal operator is bounded on the variable exponent Lebesgue space $L^{p(\cdot)/p_0}(\mathbb R^n)$. In this article, via investigating relations between boundary valued of harmonic functions on the upper half space and elements of variable exponent Hardy spaces $H^{p(\cdot)}(\mathbb R^n)$ introduced by E. Nakai and Y. Sawano and, independently, by D. Cruz-Uribe and L.-A. D. Wang, the authors characterize $H^{p(\cdot)}(\mathbb R^n)$ via the first order Riesz transforms when $p_-\in (\frac{n-1}n,\infty)$, and via compositions of all the first order Riesz transforms when $p_-\in(0,\frac{n-1}n)$., 24 pages, Submitted

Our aim in this paper is to show that the Riesz potential operator I α ( ⋅ ) of variable order α ( ⋅ ) embeds from variable exponent Morrey spaces L p ( ⋅ ) , ν ( ⋅ ) ( G ) to Campanato–Morrey spaces in the case α ( x ) p ( x ) = ν ( x ) . Our result extends the recent work of Rafeiro and Samko (2019) and the authors (Mizuta et al. 2020). We show that I α ( ⋅ ) embeds from Morrey spaces L Φ , ν ( ⋅ ) ( G ) of the double phase functionals Φ ( x , t ) = t p ( x ) + ( b ( x ) t ) q ( x ) to Campanato–Morrey spaces, where p ( ⋅ ) and q ( ⋅ ) satisfy log-Holder conditions, p ( x ) q ( x ) and b ( ⋅ ) is nonnegative, bounded and Holder continuous of order θ ∈ ( 0 , 1 ] . We also discuss the continuity of Riesz potentials I α ( ⋅ ) f of functions in L Φ , ν ( ⋅ ) ( G ) and show that I α ( ⋅ ) embeds from L Φ , ν ( ⋅ ) ( G ) to vanishing Campanato–Morrey spaces.

On the dyadic martingales, Chao and Ombe (1985) proved the L p - L q boundedness of the fractional integrals I α and their commutators [ b , I α ] , where b is in BMO or Lipschitz spaces. We extend these results to L Φ - L Ψ boundedness of generalized fractional integrals I γ and their commutators [ b , I γ ] , where L Φ and L Ψ are Orlicz spaces and b is in generalized martingale Campanato spaces on more general martingales. We also prove the L Φ - F L Ψ ϕ boundedness of [ b , I γ ] , where F L Ψ ϕ is the Triebel-Lizorkin-Orlicz space. Moreover, we characterize b such that the commutator is bounded or compact.

OBJECT Wilms’ tumor 1 (WT1) peptide vaccination is considered a potentially effective therapy against malignant glioma. We conducted a Phase I/II study to investigate the safety and feasibility of novel WT1 peptide (W10) vaccination therapy for patients with newly diagnosed malignant glioma. METHODS WT1 vaccination therapy was performed for patients with malignant glioma who have undergone concurrent radiotherapy and temozolomide therapy. A mixture of WT1 peptide with inactivated pertussis whole cell vaccine was injected intradermally once a week for at least 12 weeks. RESULTS Twenty-seven patients (12 men, 15 women; median 65 years) with the following tumors were enrolled: WHO grade IV (15), WHO grade III (12). PFS and OS of glioblastoma cases were 12.7 months 21.9 months, respectively. PFS of the MGMT unmethylated group was shorter than the methylated group. Interestingly enough, overall survival in the MGMT unmethylated group was not significantly different from the methylated group. Analysis of recurrent cases after immunotherapy showed decreased expression of WT1 antigen and increased Treg. They were suggested as a cause of treatment resistance. No serious adverse events were observed except for Grade 1 erythema at the injection sites. CONCLUSIONS This study of a novel WT1 vaccination therapy demonstrated safety and feasibility in the management of newly diagnosed malignant gliomas.

Let $\mu$ be a non-negative Radon measure satisfying the polynomial growth condition. In this paper, the authors characterize the set of pointwise multipliers on a BMO type space $\operatorname{RBMO}(\mu)$ introduced by Tolsa.

We investigate the commutators $[b,I_{\rho}]$ of generalized fractional integral operators $I_{\rho}$ with functions $b$ in generalized Campanato spaces and give a necessary and sufficient condition for the boundedness of the commutators on Orlicz spaces. To do this we define Orlicz spaces with generalized Young functions and prove the boundedness of generalized fractional maximal operators on the Orlicz spaces., Comment: 27 pages

We characterize the pointwise multipliers from a weak Orlicz space to another weak Orlicz space., Comment: 17 pages

In the present paper, we shall give a necessary and sufficient condition for the weak/strong boundedness of generalized fractional maximal operators on generalized Orlicz–Morrey spaces. We also give necessary and sufficient conditions for the vector-valued inequalities of the Hardy–Littlewood maximal operator, generalized fractional maximal operators and singular integral operators on these function spaces.

Cancer stem cells (CSCs) are the sole population possessing high self-renewal activity in tumors, with their existence affecting tumor recurrence. However, the invasive activity of CSCs has yet to be fully understood. In this article, we established a tumor sphere culture of RSV-M mouse glioma cells (RSV-M-TS) and evaluated their migration and invasion activities. Histological analysis of a tumor formed by cranial injection of the RSV-M-TS cells showed highly invasive properties and similarities with human malignant glioma tissues. When the migration activity of both RSV-M and RSV-M-TS cells were compared by intracranial injection, rapid migration of RSV-M-TS cells was observed. To confirm the invasive capabilities of RSV-M-TS cells, a three-dimensional collagen invasion assay was performed in vitro using RSV-M, RSV-M-TS, and RSV-M-TS cells cultured with medium containing serum. RSV-M and RSV-M-TS cultured with medium containing serum for 8 days indicated low migration activity, while moderate invasion activity was observed in RSV-M-TS cells. This activity was further enhanced by incubation with medium containing serum overnight. To identify the genes involved in this invasion activity, we performed quantitative polymerase chain reaction (PCR) array analysis of RSV-M and RSV-M-TS cells. Of 84 cancer metastasis-related genes, up-regulation was observed in 24 genes, while 4 genes appeared to be down-regulated in RSV-M-TS cells. These results suggest that the enhanced invasive activity of glioma sphere cells correlates with a number of tumor metastasis-related genes and plays a role in the dissemination and invasion of glioma cells.

Some new properties concerning BLO martingales are given. The BMO-BLO boundedness of martingale maximal functions and Bennett type characterization of BLO martingales are shown. Also, a non-negative BMO martingale that is not in BLO is constructed.

In this paper we characterize pointwise multipliers from a Musielak-Orlicz-Morrey space to another Musielak-Orlicz-Morrey space. The set of all pointwise multipliers is also a Musielak-Orlicz-Morrey space.

We establish the theory of Orlicz-Hardy spaces generated by a wide class of functions. The class will be wider than the class of all the N-functions. In particular, we consider the non-smooth atomic decomposition. The relation between Orlicz-Hardy spaces and their duals is also studied. As an application, duality of Hardy spaces with variable exponents is revisited. This work is different from earlier works about Orlicz-Hardy spaces H Φ(ℝ n ) in that the class of admissible functions ϕ is largely widened. We can deal with, for example, $$\Phi (r) \equiv \left\{ \begin{gathered} r^{p1} \left( {\log \left( {e + {1 \mathord{\left/ {\vphantom {1 r}} \right. \kern-\nulldelimiterspace} r}} \right)} \right)^{q1} , 0 < r \leqslant 1, \hfill \\ r^{p2} \left( {\log \left( {e + r} \right)} \right)^{q2} , r > 1, \hfill \\ \end{gathered} \right.$$ with p 1, p 2 ∈ (0,∞) and q 1, q 2 ∈ (−∞,∞), where we shall establish the boundedness of the Riesz transforms on H Φ(ℝ n ). In particular, ϕ is neither convex nor concave when 0 < p 1 < 1 < p 2 < ∞, 0 < p 2 < 1 < p 1 < ∞ or p 1 = p 2 = 1 and q 1, q 2 > 0. If Φ(r) ≡ r(log(e+r)) q , then H Φ(ℝ n ) = H(log H) q (ℝ n ). We shall also establish the boundedness of the fractional integral operators I α of order α ∈ (0,∞). For example, I α is shown to be bounded from H(log H)1 − α/n (ℝ n ) to L n/(n − α)(log L)(ℝ n ) for 0 < α < n.

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We present some characterizations for the boundedness of the generalized fractional integral operators on Morrey spaces. The characterizations follow from two key estimates, one for the norm of some functions in Morrey spaces, and another for the values of the corresponding fractional integrals. We prove three theorems about necessary and sufficient conditions. We show that these theorems are independent by giving some examples. We also obtain counterparts for the weak generalized Morrey spaces.

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