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Embedding Theorems for Mixed Norm Spaces and Applications
Karlstad University, Faculty of Technology and Science, Avdelningen för matematik.
2008 (English)Licentiate thesis, monograph (Other scientific)
Abstract [en]

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.

Place, publisher, year, edition, pages
Karlstad: Karlstad University , 2008. , p. 63
Series
Karlstad University Studies, ISSN 1403-8099 ; 2008:31
Keywords [en]
mixed norms, embeddings, rearrangements, anisotropic fractional Sobolev spaces, anisotropic Besov spaces
Keywords [sv]
mixade normer, inbäddningar, omarrangeringar, anisotropa fractionära Sobolev rum, anisotropa Besov rum
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-2874ISBN: 978-91-7063-190-0 (print)OAI: oai:DiVA.org:kau-2874DiVA, id: diva2:54555
Presentation
2008-10-17, 21A 342, Karlstads universitet, Karlstad, 13:15 (Swedish)
Opponent
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Available from: 2008-10-17 Created: 2008-10-17 Last updated: 2011-10-04Bibliographically approved

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Algervik, Robert

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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