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Embedding Theorems for Mixed Norm Spaces and Applications
Karlstads universitet, Fakulteten för teknik- och naturvetenskap, Avdelningen för matematik.
2008 (engelsk)Licentiatavhandling, monografi (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Karlstad: Karlstad University , 2008. , s. 63
Serie
Karlstad University Studies, ISSN 1403-8099 ; 2008:31
Emneord [en]
mixed norms, embeddings, rearrangements, anisotropic fractional Sobolev spaces, anisotropic Besov spaces
Emneord [sv]
mixade normer, inbäddningar, omarrangeringar, anisotropa fractionära Sobolev rum, anisotropa Besov rum
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:kau:diva-2874ISBN: 978-91-7063-190-0 (tryckt)OAI: oai:DiVA.org:kau-2874DiVA, id: diva2:54555
Presentation
2008-10-17, 21A 342, Karlstads universitet, Karlstad, 13:15 (svensk)
Opponent
Veileder
Tilgjengelig fra: 2008-10-17 Laget: 2008-10-17 Sist oppdatert: 2011-10-04bibliografisk kontrollert

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