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Compactness of higher-order Sobolev embeddings
Slavíková, Lenka ; Pick, Luboš (advisor) ; Nekvinda, Aleš (referee)
The present work deals with m-th order compact Sobolev embeddings on a do- main Ω ⊆ Rn endowed with a probability measure ν and satisfying certain isoperi- metric inequality. We derive a condition on a pair of rearrangement-invariant spaces X(Ω, ν) and Y (Ω, ν) which suffices to guarantee a compact embedding of the Sobolev space V m X(Ω, ν) into Y (Ω, ν). The condition is given in terms of compactness of certain operator on representation spaces. This result is then applied to characterize higher-order compact Sobolev embeddings on concrete measure spaces, including John domains, Maz'ya classes of Euclidean domains and product probability spaces, among them the Gauss space is the most stan- dard example. 1
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The Creation and Implementation of a School Education Programme in Practice
Chalupník, Milan ; Trojan, Václav (advisor) ; Slavíková, Lenka (referee)
This final bachelor thesis deals with problems of creation process of school education programs in primary schools in Czech Republic. Since it is an activity that school subjects could not have experienced so far and since the availability of pilot schools outcomes is not optimal, this thesis aims to provide basic information file that is important for start of systematic work on creation of school curriculum document. It systematizes correlation between School Education Program and actual legal rules of Czech legal system and offers instruments for motivation of participants making this document. The important part of the thesis is also research. The aim of this research was to judge factors that have influence on creation process of School Education Program in primary schools and also in terms of their difference in schools of number of students bellow 200 and over 200 pupils. The results of this research confirm that there are differences in some facts between small and large schools. These differences can subsequently influence the progress of creation process of School Education Program and thus could have essential influence on its final form in terms of qualitative judgement and above all in terms of its function.
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Sexual harassment in the Czech university environment from the female students' perspective- qualitative probe
Slavíková, Lenka ; Pavlík, Petr (advisor) ; Vohlídalová, Marta (referee)
The master thesis "Sexual harassment in the Czech university environment from the female students' perspective- qualitative probe" focuses on how students perceive sexual and gender harassment and what their experiences with it are at the Czech universities. The theoretical part contains explanations of important terms, discusses definitions of sexual harassment, further considers power topics related to sexual harassment, points to who is harassed and why and finally, shows specialities of the university environment including prevention of sexual harassment. The empirical part introduces qualitative research- semi-structured interviews about sexual harassment with 18 female students of Czech universities. It interprets several important topics, in particular: definitions of sexual and gender harassment, experiences with it and reactions to it, power, fear, relations between teachers and students, alcohol, (non)talking about sexual harassment etc.
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Princip nákladové přiměřenosti v právních předpisech EU v oblasti životního prostředí: ponaučení z implementace ochrany vod a ovzduší
Brabec, Jan ; Jílková, Jiřina (advisor) ; Knápek, Jaroslav (referee) ; Slavíková, Lenka (referee)
Environmental legislation in the European Union recognizes the principle of proportionality as a tool that helps identify cases that require spending of disproportionate resources to achieve environmental targets. If economic costs of achieving a certain target are significantly higher than associated benefits, an exemption may be granted to prevent wasting resources on measures with only a negligible effect on the environment. The principle is well established in water protection by means of the Water Framework Directive (2000/60/EC) and in air protection through the Industrial Emissions Directive (2010/75/EU). In theory, such setting should ensure more efficient and robust water and air protection. However, with no unified methodology and a high level of discretion given to individual member states, the process of assessing proportionality has become very heterogenous. As a result, methodologies used across Europe often differ from each other significantly, possibly distorting the original idea of equal treatment of European water bodies and sources of air pollution. The goal of this thesis is to determine whether the use of the proportionality principle in water and air protection contributes to more efficient environmental protection in the EU and whether the principle is used consistently in...
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Weighted inequalities and properties of operators and embeddings on function spaces
Slavíková, Lenka ; Pick, Luboš (advisor)
The present thesis is devoted to the study of various properties of Banach func- tion spaces, with a particular emphasis on applications in the theory of Sobolev spaces and in harmonic analysis. The thesis consists of four papers. In the first one we investigate higher-order embeddings of Sobolev-type spaces built upon rearrangement-invariant Banach function spaces. In particular, we show that optimal higher-order Sobolev embeddings follow from isoperimetric inequal- ities. In the second paper we focus on the question when the above-mentioned Sobolev-type space is a Banach algebra with respect to a pointwise multiplica- tion of functions. An embedding of the Sobolev space into the space of essentially bounded functions is proved to be the answer to this question in several standard as well as nonstandard situations. The third paper is devoted to the problem of validity of the Lebesgue differentiation theorem in the context of rearrangement- invariant Banach function spaces. We provide a necessary and sufficient condition for the validity of this theorem given in terms of concavity of certain functional depending on the norm in question and we find also alternative characterizations expressed in terms of properties of a maximal operator related to the norm. The object of the final paper is the boundedness of the...
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Weighted inequalities and properties of operators and embeddings on function spaces
Slavíková, Lenka ; Pick, Luboš (advisor) ; Pérez, Carlos (referee) ; Malý, Jan (referee)
The present thesis is devoted to the study of various properties of Banach func- tion spaces, with a particular emphasis on applications in the theory of Sobolev spaces and in harmonic analysis. The thesis consists of four papers. In the first one we investigate higher-order embeddings of Sobolev-type spaces built upon rearrangement-invariant Banach function spaces. In particular, we show that optimal higher-order Sobolev embeddings follow from isoperimetric inequal- ities. In the second paper we focus on the question when the above-mentioned Sobolev-type space is a Banach algebra with respect to a pointwise multiplica- tion of functions. An embedding of the Sobolev space into the space of essentially bounded functions is proved to be the answer to this question in several standard as well as nonstandard situations. The third paper is devoted to the problem of validity of the Lebesgue differentiation theorem in the context of rearrangement- invariant Banach function spaces. We provide a necessary and sufficient condition for the validity of this theorem given in terms of concavity of certain functional depending on the norm in question and we find also alternative characterizations expressed in terms of properties of a maximal operator related to the norm. The object of the final paper is the boundedness of the...
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