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Skorokompaktní vnoření prostorů funkcí
Křepela, Martin ; Pick, Luboš (advisor) ; Spurný, Jiří (referee)
This work is dealing with almost-compact embeddings of function spaces, in particular, the class of classical and weak Lorentz spaces with a norm given by a general weight fuction is studied. These spaces are not Banach function spaces in general, thus the almost-compact em- bedding is defined for more general sturctures of rearrangement-invariant lattices. A general characterization of when an r.i. lattice is almost-compactly embedded into a Lorentz space, involving an optimal constant of a certain continuous embedding, is proved. Based on this the- orem and appropriate known results about continuous embeddings, explicit characterizations of mutual almost-compact embeddings of all subtypes of Lorentz spaces are obtained. 1
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Integral and supremal operators on weighted function spaces
Křepela, Martin ; Pick, Luboš (advisor) ; Sickel, Winfried (referee) ; Tichonov, Sergey (referee)
Title: Integral and Supremal Operators on Weighted Function Spaces Author: Martin Křepela Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Luboš Pick, CSc., DSc., Department of Mathematical Analysis Abstract: The common topic of this thesis is boundedness of integral and supre- mal operators between function spaces with weights. The results of this work have the form of characterizations of validity of weighted operator inequalities for appropriate cones of functions. The outcome can be divided into three cate- gories according to the particular type of studied operators and function spaces. The first part involves a convolution operator acting on general weighted Lorentz spaces of types Λ, Γ and S defined in terms of the nonincreasing rear- rangement, Hardy-Littlewood maximal function and the difference of these two, respectively. It is characterized when a convolution-type operator with a fixed kernel is bounded between the aforementioned function spaces. Furthermore, weighted Young-type convolution inequalities are obtained and a certain optima- lity property of involved rearrangement-invariant domain spaces is proved. The additional provided information includes a comparison of the results to the pre- viously known ones and an overview of basic properties of some new function spaces...
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Integral and supremal operators on weighted function spaces
Křepela, Martin ; Pick, Luboš (advisor) ; Sickel, Winfried (referee) ; Tichonov, Sergey (referee)
Title: Integral and Supremal Operators on Weighted Function Spaces Author: Martin Křepela Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Luboš Pick, CSc., DSc., Department of Mathematical Analysis Abstract: The common topic of this thesis is boundedness of integral and supre- mal operators between function spaces with weights. The results of this work have the form of characterizations of validity of weighted operator inequalities for appropriate cones of functions. The outcome can be divided into three cate- gories according to the particular type of studied operators and function spaces. The first part involves a convolution operator acting on general weighted Lorentz spaces of types Λ, Γ and S defined in terms of the nonincreasing rear- rangement, Hardy-Littlewood maximal function and the difference of these two, respectively. It is characterized when a convolution-type operator with a fixed kernel is bounded between the aforementioned function spaces. Furthermore, weighted Young-type convolution inequalities are obtained and a certain optima- lity property of involved rearrangement-invariant domain spaces is proved. The additional provided information includes a comparison of the results to the pre- viously known ones and an overview of basic properties of some new function spaces...
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Skorokompaktní vnoření prostorů funkcí
Křepela, Martin ; Pick, Luboš (advisor) ; Spurný, Jiří (referee)
This work is dealing with almost-compact embeddings of function spaces, in particular, the class of classical and weak Lorentz spaces with a norm given by a general weight fuction is studied. These spaces are not Banach function spaces in general, thus the almost-compact em- bedding is defined for more general sturctures of rearrangement-invariant lattices. A general characterization of when an r.i. lattice is almost-compactly embedded into a Lorentz space, involving an optimal constant of a certain continuous embedding, is proved. Based on this the- orem and appropriate known results about continuous embeddings, explicit characterizations of mutual almost-compact embeddings of all subtypes of Lorentz spaces are obtained. 1
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Competitive Men Bodybuilding as Seen by the Public
Křepela, Martin ; Stackeová, Daniela (advisor) ; Rychtecký, Antonín (referee)
Název: Soutěžní kulturistika mužů v očích veřejnosti. Competitive men bodybuilding in the eyes of public. Cíle práce: Vytvoření a standardizace dotazníku ke zjišťování postojů veřejnosti k soutěžní kulturistice mužů. Analýza postojů pražské veřejnosti k soutěžní kulturistice mužů. Metoda: Postoje byly zjišťovány pomocí standardizovaného dotazníku u 127 občanů hlavního města Prahy. Dotazník se zabýval postoji kjednotlivým aspektům soutěžní kulturistiky. Velká pozornost byla věnována vývoji a standardizaci dotazníku (inventáře). K tomuto účelu byly použity sofistikované vícerozměrné statistické metody (například faktorová analýza). Výsledky: Výsledky analyzují a srovnávají postoje sledovaného souboru pražské veřejnosti k soutěžní kulturistice mužů. Klíčová slova: kulturistika, postoje, tvorba dotazníku, faktorová analýza
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