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The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $\mathbb R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order $s\in (0,1)$, and higher-order spaces are considered. Related Hardy type inequalities are proposed as well. An extension theorem is proved, that enables us to derive embeddings for spaces defined in Lipschitz domains. Necessary and sufficient conditions for the compactness of fractional Orlicz-Sobolev embeddings are provided.

Although private or community initiatives for biodiversity conservation (such as land trusts) have a strong tradition in many countries, rigorous evidence of recently evolved movements in post-socialist countries is missing. This study describes the evolution of Czech land trust movement and analyses their representatives’ motivation for engagement in biodiversity conservation. It also investigates the intensity of interaction among public and land trust conservation efforts. For this purpose, we identified localities in which the territory managed by Czech land trusts overlaps with small-scale public nature reserves managed by regional governments. We conducted semi-structured face-to-face interviews with representatives of all NGOs and regional officials in-charge. Our qualitative analysis revealed that some regional biodiversity conservation officials see land trusts as partners, but others are rather indifferent to, or uninformed about, their activities. Additionally, land trust representatives see themselves as complementing the public effort: their main motivation for engagement is to facilitate biodiversity conservation in addition to the public provision.

International audience; The major event that hit Europe in summer 2021 reminds society that floods are recurrent and among the costliest and deadliest natural hazards. The long-term flood risk management (FRM) efforts preferring sole technical measures to prevent and mitigate floods have shown to be not sufficiently effective and sensitive to the environment. Nature-Based Solutions (NBS) mark a recent paradigm shift of FRM towards solutions that use nature-derived features, processes and management options to improve water retention and mitigate floods. Yet, the empirical evidence on the effects of NBS across various settings remains fragmented and their implementation faces a series of institutional barriers. In this paper, we adopt a community expert perspective drawing upon LAND4FLOOD Natural flood retention on private land network (https://www.land4flood.eu) in order to identify a set of barriers and their cascading and compound interactions relevant to individual NBS. The experts identified a comprehensive set of 17 barriers affecting the implementation of 12 groups of NBS in both urban and rural settings in five European regional environmental domains (i.e., Boreal, Atlantic, Continental, Alpine-Carpathian, and Mediterranean). Based on the results, we define avenues for further research, connecting hydrology and soil science, on the one hand, and land use planning, social geography and economics, on the other. Our suggestions ultimately call for a transdisciplinary turn in the research of NBS in FRM.

Implementing the Climate-Smart Forestry (CSF) concept into practice requires interaction among key stakeholders, especially forest owners and managers, policymakers (or regulators in general), forest consultants, and forest users. But what could be the most effective policy instruments to achieve climate smartness in mountain forests? Which ones would be the most acceptable for forest owners? And for the local forest communities? Should they be designed and implemented with the use of participatory approaches or rather on a top-down basis? This chapter summarizes key policy instruments structured in three subsequent categories: command-and-control, voluntary market-based instruments, and community cooperation. It provides examples of their functioning in the forestry sector and discusses their suitability for the implementation of climate smart forestry. It appears that there are many policy instruments used with varying degrees of success such as forest concessions or voluntary certification schemes. A wide range of instruments are responding to direct regulation; this has been seen as insufficient to deal with natural hazards and calamities.

Nature-based solutions (NbS) are often framed positively in terms of win–win options or no-regret measures. However, are NbS equally beneficial for everyone? Are burdens and benefits of NbS really equally distributed and projects embraced by everyone? Is the process leading to the implementation of NbS always fair and inclusive? This chapter provides a broad overview of different environmental justice issues, critically reflecting on NbS through recognition justice, procedural justice, and distributive justice. Whereas the current critical literature focuses particularly on urban NbS, this chapter focuses on the wider translocal consequences of NbS projects. The theoretical reflections are illustrated with case studies of NbS from various countries: the recognition of marginalised women in Vietnam in mangrove restoration projects, the challenges when introducing procedural justice in implementing NbS in Serbia, the legal injustices locals are faced in the Czech Republic when they want to implement NbS, the trade-off between public collective and individual economic interest when implementing a sand nourishment project in the Netherlands, and the development of a beneficiary-pays based upstream–downstream compensation scheme in Austria.

We discuss the Hormander multiplier theorem for Lp boundedness of Fourier multipliers in which the multiplier belongs to a fractional Sobolev space with smoothness s. We show that this theorem does not hold in the limiting case |1/p−1/2|=s/n.

It is well known that the Hormander smoothness condition sup y ≠ 0 ⁡ ∫ | x | ≥ 2 | y | | K ( x − y ) − K ( x ) | d x ∞ implies weak-type ( 1 , 1 ) estimates for associated L 2 -bounded Calderon–Zygmund operators. It has been an open question to know whether Hormander's condition also suffices to guarantee weak-type ( 1 , 1 , 1 / 2 ) estimates for bilinear Calderon–Zygmund operators that are bounded at one point. In this paper, we provide a negative answer to this question.

The reflection of ecosystem services in environmental policy has recently become a key aspect in solving environmental problems occurring as a consequence of their overburdening. However, decision makers often pay attention predominantly to results of quantitative (monetary valuation) methods. This article explores a new way of combining quantitative and qualitative methods that has proven to be a useful practice for achieving better environmental governance. We combine the (quantitative) choice experiment method and (qualitative) institutional analysis as full and equal complements. In our approach, the goal of qualitative institutional analysis is not to verify the adequacy of willingness-to-pay results but rather to better address cultural and social perspectives of society representatives. Such an approach increases the robustness of policy recommendations and their acceptance in comparison with isolated applications of both methods. To verify this general premise, both methods were applied in the territory of the Eastern Ore Mountains in the Czech Republic to capture preferences and attitudes of local stakeholders as well as tourists towards small-scale ecosystems. The results confirm that preference calculations regarding aesthetic values of ecosystems need to be complemented with facts about institutional settings and barriers in order to better address locally relevant recommendations for decision makers, such as the introduction of new economic instruments (e.g., local taxes or entrance fees). The findings of this study can also be considered for governance of larger local, common-pool resources such as (public) forests or protected areas.

Some recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings. The limits of these spaces when the smoothness parameter $$s\in (0,1)$$ s ∈ ( 0 , 1 ) tends to either of the endpoints of its range are also discussed. This note is based on recent papers of ours, where additional material and proofs can be found.

The European Union (EU) Water Framework Directive (WFD) requires EU member states to produce and implement river basin management plans, which are to be designed and updated via participatory processes that inform, consult with, and actively involve all interested stakeholders. The assumption of the European Commission is that stakeholder participation, and institutional adaptation and procedural innovation to facilitate it, are essential to the effectiveness of river basin planning and, ultimately, the environmental impact of the Directive. We analyzed official documents and the WFD literature to compare implementation of the Directive in EU member states in the initial WFD planning phase (2000-2009). Examining the development of participatory approaches to river basin management planning, we consider the extent of transformation in EU water governance over the period. Employing a mixed quantitative and qualitative approach, we map the implementation "trajectories" of 13 member states, and then provide a detailed examination of shifts in river basin planning and participation in four member states (Germany, Sweden, Poland and France) to illustrate the diversity of institutional approaches observed. We identify a general tendency towards increased, yet circumscribed, stakeholder participation in river basin management in the member states examined, alongside clear continuities in terms of their respective pre-WFD institutional and procedural arrangements. Overall, the WFD has driven a highly uneven shift to river basin-level planning among the member states, and instigated a range of efforts to institutionalize stakeholder involvement-often through the establishment of advisory groups to bring organized stakeholders into the planning process.

Flood resilience (resilient flood risk management), which has been repeatedly demanded, can be achieved through the phases of the risk management cycle. There is a vast body of literature on adaptation, disaster risk reduction measures, and effectiveness of prevention, seen through the lens of postdisaster recovery, but oftentimes the existing literature seems to underestimate the impact of financial flood recovery schemes on resilient recovery of individual households in particular. This contribution focuses on how financial schemes for flood damage compensations—their sources, design, and timing—shape the resilience of recovery of individual households. It discusses the dilemma of recovery of whether recovery schemes should be used strategically to increase resilience, or rather serve early restoration needs, equality access issues, and so on. This contribution seeks to unify the current fragmented academic debate on household resilient recovery by focusing on the ambiguous role of financial recovery schemes. This article is categorized under: Engineering Water > Planning Water Human Water > Value of Water.

Options for the increase of flood resilience during the recovery phase is, to a large extent, overlooked. The special issue Financial Schemes for Resilient Flood Recovery investigates how the implementation of financial schemes (government relief subsidies, insurance schemes, buy-outs, etc.) might increase flood resilience. Five papers address following questions: Shall government relief subsidies exist when there is flood insurance in place, and, if so, how might they both be coordinated? Where (or how) to decide about build back better incentives and where to go for planned relocation programs? What is the distributional equity of financial schemes for flood recovery, and has it been sufficiently treated?.

Given a bounded measurable function $\sigma$ on $\mathbb{R}^n$, we let $T_\sigma $ be the operator obtained by multiplication on the Fourier transform by $\sigma $. Let $0

We provide a complete proof of an optimal version of the Marcinkiewicz multiplier theorem and discuss a relevant example.

Main topic of this article is focused on the leading and managing schools as a learning organizations. The fi rst part is orientated on the brief characteristic of the learning organization in the relationship with the requirements of the employment market on the school leaders competences. Second part reviews various attitudes to the creation of the schools as a learning organization from leader and manager, team management and change management point of view.

We provide an improvement of the Hörmander multiplier theorem in which the Sobolev space ${{L^{r}_{s}}}(\mathbb R^{n})$ with integrability index r and smoothness index s > n/r is replaced by the Sobolev space with smoothness s built upon the Lorentz space $L^{n/s,1}(\mathbb R^{n})$.

Nature-based solutions (NBS) have recently spread to the flood risk management (FRM) agenda as potentially efficient and sustainable measures to reduce the susceptibility to and impacts of various kinds of floods. The aim of this chapter is to introduce the roots of various conceptualizations of scale, the way they are encountered, and the implications different views of scale may have on the use of NBS in FRM.

Do landowners realize (and privately fund) natural water retention measures (NWRM) on their own land? Why? And how are they capable of assessing the hydrological and ecological effects of these measures? The Czech case study presents the story of an individual farmer who decided to invest his private resources in water retention and biodiversity enhancement while continuing his farming practices. We describe the historical and geographical background of the case study as well as the farmer’s motivations and beliefs. We also discuss the scaling-up potential of the presented case. Information for the case study was gathered with a mixed-methodology approach that combined official statistical sources of cadastral records, content analyses of local media articles, a field survey and communication with the farmer during an excursion to his farm. The intention is to show the alternative when considering NWRM implementation. This alternative is heading the same direction as public subsidy schemes. Private initiatives may support (instead of undermine) public policy goals, and they are often faster and cheaper.

Sobolev embeddings, of arbitrary order, are considered into function spaces on domains of $\mathbb R^n$ endowed with measures whose decay on balls is dominated by a power $d$ of their radius. Norms in arbitrary rearrangement-invariant spaces are contemplated. A comprehensive approach is proposed based on the reduction of the relevant $n$-dimensional embeddings to one-dimensional Hardy-type inequalities. Interestingly, the latter inequalities depend on the involved measure only through the power $d$. Our results allow for the detection of the optimal target space in Sobolev embeddings, for broad families of norms, in situations where customary techniques do not apply. In particular, new embeddings, with augmented target spaces, are deduced even for standard Sobolev spaces., Comment: to appear in Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire

Nature-based solutions (NBS) in Flood Risk Management require more—and mostly privately owned—land, and more diverse stakeholder involvement than traditional (grey) engineering approaches. This also implies that there are challenges related to different disciplines. Flood risk management with NBS is an issue not only of technical expertise, but it asks for land-use planning, economics, property rights, sociology, landscape planning, ecology, hydrology, agriculture and other disciplines to cope with the challenges of implementing them. Nature-based FRM is thus an inter- and transdisciplinary endeavor.

Flood recovery is an important period in the flood risk management cycle. Recently, flood recovery has become viewed as an opportunity for future flood damage mitigation. Financial flows to cover flood damages and rules regarding their allocation are crucial for supporting or undermining mitigation efforts. In this paper, we map and compare state flood recovery funding in the so-called Visegrad Group Countries (V4), i.e. Czechia, Hungary, Poland and Slovakia, over the past 30 years of their democratic history. We apply a qualitative comparative approach to identify differences and similarities in risk sharing and state flood recovery funding approaches among these countries. Additionally, we reveal how risk sharing is addressed by existing flood recovery funding schemes. The results indicate that national governments have a low willingness to institutionalise ex-ante compensation schemes. Ad hoc instruments initiated shortly after disastrous flooding usually do not provide incentives to reduce future flood damages.

We investigate two types of boundedness criteria for bilinear Fourier multiplier operators with symbols with bounded partial derivatives of all (or sufficiently many) orders. Theorems of the first type explicitly prescribe only a certain rate of decay of the symbol itself while theorems of the second type require, in addition, the same rate of decay of all derivatives of the symbol. We show that even though these two types of bilinear multiplier theorems are closely related, there are some fundamental differences between them which arise in limiting cases. Also, since theorems of the latter type have so far been studied mainly in connection with the more general class of bilinear pseudodifferential operators, we revisit them in the special case of bilinear Fourier multipliers, providing also some improvements of the existing results in this setting.

Environmental information disclosure instruments inevitably also carry information costs. It is important to pay attention to these costs because of the competitiveness issues connected with the regulatory burden of the private sector or the overall cost-effectiveness of different types of environmental regulation from the public sector point of view. We undertake an ex-post analysis to quantify and analyse reporting costs of private sector induced by the European Pollutant Release and Transfer Register (E-PRTR). We focus on the case of the Czech Republic. The average annual reporting costs, additional to other reporting duties, are € 365 per facility. The Czech PRTR comprises 8 times more facilities than required by the European law, and thereby increases correspondingly the total reporting costs. The best predictor variable of the costs is the need for measuring or calculating additional releases or transfers beyond the information requirements of other registers.

We study the necessity of bump conditions for the boundedness of the Hardy-Littlewood maximal operator $M$ from $L^p(v)$ into $L^p(w)$, where $1

Embedding theorems for Orlicz-Sobolev spaces into Orlicz or Orlicz-Lorentz spaces in domains in R n , endowed with a Frostman measure, are offered. Parallel embeddings for Lorentz-Sobolev spaces into (generalized) Lorentz spaces are also established. The relevant embeddings yield an optimal target norm, in the relevant classes, whenever it does exist. In particular, various results available in the literature are improved by special choices of the function spaces and of the measure.

A version of the Lebesgue differentiation theorem is offered, where the [Formula: see text] norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation theorem are established. In particular, Lorentz, Orlicz and other customary norms for which Lebesgue’s theorem holds are characterized.

The paper deals with terminological issues within economics of the environment as used in Czech socio-economic research. In particular, it criticises the misuse of the term “environmental economics” in the context of Simon and Lomborg’s criticism of the Club of Rome reports. In reaction to recent research papers [such as Louzek, 2013], it argues that the neoclassical anchor of environmental economics needs to be reflected when discussing various applications of economics to environmental problems.

A comprehensive approach to Sobolev type embeddings, involving arbitrary rearrangement-invariant norms on the entire Euclidean space \begin{document}${\mathbb R^n}$\end{document} , is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in our analysis is a new reduction principle for the relevant embeddings, showing their equivalence to a couple of considerably simpler one-dimensional inequalities. Applications to the classes of the Orlicz-Sobolev and the Lorentz-Sobolev spaces are also presented. These contributions fill in a gap in the existing literature, where sharp results in such a general setting are only available for domains of finite measure.

Economics of the environment as an applied field of economics was established during the 1960s. At the time of its foundation, neoclassical environmental economics represented the mainstream view regarding the explanation of the causes of environmental problems and their solutions. Since then, however, two other competing approaches - the free market and institutional ecological economics - have evolved. These two new approaches present different analytical focuses as they stress the role of institutions (property rights and/or management regimes) in environmental protection. As a result, environmental research based on cost-benefit analysis was substituted by the application of various forms of institutional (often qualitative) analyses. The goal of the paper is to justify the importance of this methodological shift that is sometimes minimized by mainstream economists. The research focus of competing approaches and their methods are mapped through comparative analysis, and the theoretical description is connected with the practical examples of the EU environmental policy.

The commentary defends the central idea of current institutional social research - that institutions are significant variables influencing the human action regarding the resource allocation. This idea was strongly opposed by the scientific board of the Czech economic faculty (institutionally oriented economic research was labeled as needless). The goal is to open the debate about this issue and ask the opponents to formulate concrete objections. Theoretical arguments and empirical examples are raised in favor of the institutional economics.

The paper contains a descriptive analysis of selected interdisciplinary research methods developed for the study of complex socio-ecological systems (climate change problems in particular). Institutional analysis and participatory methods of social consensus are in the centre of the focus.

Due to methodological problems and their practical limitations, the criticism of neoclassical environmental economics is increasing. The goal of this paper is to stress the differences and similarities between the two competing alternative approaches – institutional ecological economics and free-market approaches to environmental protection – to encourage their interactions towards a possible synthesis in the future.

Neoclassical environmental economics, ecological economics and free market approaches to environmental protection are currently three main schools of thoughts that are systematically focused on interactions between the society and the environment. They all have strong defenders as well as opponents. Although the environmental economics is still considered as mainstream, the critique from alternative approaches is increasing. The goal of the article is to briefly introduce main thoughts of all three schools and their interactions. The intensity of mutual interactions in the last decade was investigated via the analysis of articles published in high-rated journals.

The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$-dimensional domain, is a Banach algebra under pointwise multiplication of functions. A sharp balance condition among the order of the Sobolev space, the strength of the norm, and the (ir)regularity of the domain is provided for the relevant Sobolev space to be a Banach algebra. The regularity of the domain is described in terms of its isoperimetric function. Related results on the boundedness of the multiplication operator into lower-order Sobolev type spaces are also established. The special cases of Orlicz-Sobolev and Lorentz-Sobolev spaces are discussed in detail. New results for classical Sobolev spaces on possibly irregular domains follow as well.

Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev type inequalities of any order, involving arbitrary rearrangement-invariant norms, on open sets in R n , possibly endowed with a measure density, are reduced to much simpler one-dimensional inequalities for suitable integral operators depending on the isoperimetric function of the relevant sets. As a consequence, the optimal target space in the relevant Sobolev embeddings can be determined both in standard and in non-standard classes of function spaces and underlying measure spaces. In particular, our results are applied to any-order Sobolev embeddings in regular (John) domains of the Euclidean space, in Maz'ya classes of (possibly irregular) Euclidean domains described in terms of their isoperimetric function, and in families of product probability spaces, of which the Gauss space is a classical instance.

We study higher-order compact Sobolev embeddings on a domain $\Omega \subseteq \mathbb R^n$ endowed with a probability measure $\nu$ and satisfying certain isoperimetric inequality. Given $m\in \mathbb N$, we present a condition on a pair of rearrangement-invariant spaces $X(\Omega,\nu)$ and $Y(\Omega,\nu)$ which suffices to guarantee a compact embedding of the Sobolev space $V^mX(\Omega,\nu)$ into $Y(\Omega,\nu)$. The condition is given in terms of compactness of certain one-dimensional operator depending on the isoperimetric function of $(\Omega,\nu)$. We then apply this result to the characterization of higher-order compact Sobolev embeddings on concrete measure spaces, including John domains, Maz'ya classes of Euclidean domains and product probability spaces, whose standard example is the Gauss space.

Recently, the Czech Republic has been affected with negative impacts of hydrological extremes (such as floods and droughts). This is the reason why different types of regulation modifications have been discussed in order to address increasing water scarcity and variability throughout a year.