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Embedding Theorems ...
Embedding Theorems for Mixed Norm Spaces and Applications
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- Algervik, Robert, 1981- (author)
- Karlstads universitet,Avdelningen för matematik
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- Kolyada, Viktor, Professor (thesis advisor)
- Karlstads universitet,Fakulteten för teknik- och naturvetenskap
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- Persson, Lars-Erik, Professor (opponent)
- Institutionen för vårdvetenskap och socialt arbete, Växjö universitet
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(creator_code:org_t)
- ISBN 9789170631900
- Karlstad : Karlstad University, 2008
- English 63 s.
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Series: Karlstad University Studies, 1403-8099 ; 2008:31
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Abstract
Subject headings
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- This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of Sobolev and Besov type spaces. The work in this direction originates in a paper due to Gagliardo (1958), and was continued by Fournier (1988) and by Kolyada (2005). We consider fully anisotropic mixed norm spaces. Our main theorem states an embedding of these spaces into Lorentz spaces. Applying this result, we obtain sharp embedding theorems for anisotropic fractional Sobolev spaces and anisotropic Sobolev-Besov spaces. The methods used are based on non-increasing rearrangements and on estimates of sections of functions and sections of sets. We also study limiting relations between embeddings of spaces of different type. More exactly, mixed norm estimates enable us to get embedding constants with sharp asymptotic behaviour. This gives an extension of the results obtained for isotropic Besov spaces $B_p^\alpha$ by Bourgain, Brezis, and Mironescu, and for Besov spaces $B^{\alpha_1,\dots,\alpha_n}_p$ by Kolyada. We study also some basic properties (in particular the approximation properties) of special weak type spaces that play an important role in the construction of mixed norm spaces and in the description of Sobolev type embeddings.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- mixed norms
- embeddings
- rearrangements
- anisotropic fractional Sobolev spaces
- anisotropic Besov spaces
- mixade normer
- inbäddningar
- omarrangeringar
- anisotropa fractionära Sobolev rum
- anisotropa Besov rum
- MATHEMATICS
- MATEMATIK
- Matematik
- Mathematics
Publication and Content Type
- vet (subject category)
- lic (subject category)
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