Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings

Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x∈Ω⊂ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A=Lφ,E, B=Lψ,E, giving some...

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Main Author: Evgeniy Pustylnik
Format: Article
Language:English
Published: Wiley 2005-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2005/254184
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author Evgeniy Pustylnik
author_facet Evgeniy Pustylnik
author_sort Evgeniy Pustylnik
collection DOAJ
description Let Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x∈Ω⊂ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A=Lφ,E, B=Lψ,E, giving some optimal (or rather sharp) relations between parameter-functions φ(t) and ψ(t) and new results for embeddings of Orlicz-Sobolev spaces.
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publishDate 2005-01-01
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series Journal of Function Spaces and Applications
spelling doaj-art-28075a429d5c4ebc8dfc1f4a0500a22c2025-08-20T03:54:42ZengWileyJournal of Function Spaces and Applications0972-68022005-01-013218320810.1155/2005/254184Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddingsEvgeniy Pustylnik0Department of Mathematics, Technion—Israel Institute of Technology, Haifa 32000, IsraelLet Dkf mean the vector composed by all partial derivatives of order k of a function f(x), x∈Ω⊂ℝn. Given a Banach function space A, we look for a possibly small space B such that ‖f‖B≤c‖|Dkf|‖A for all f∈C0k(Ω). The estimates obtained are applied to ultrasymmetric spaces A=Lφ,E, B=Lψ,E, giving some optimal (or rather sharp) relations between parameter-functions φ(t) and ψ(t) and new results for embeddings of Orlicz-Sobolev spaces.http://dx.doi.org/10.1155/2005/254184
spellingShingle Evgeniy Pustylnik
Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings
Journal of Function Spaces and Applications
title Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings
title_full Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings
title_fullStr Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings
title_full_unstemmed Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings
title_short Sobolev type inequalities in ultrasymmetric spaces with applications to Orlicz-Sobolev embeddings
title_sort sobolev type inequalities in ultrasymmetric spaces with applications to orlicz sobolev embeddings
url http://dx.doi.org/10.1155/2005/254184
work_keys_str_mv AT evgeniypustylnik sobolevtypeinequalitiesinultrasymmetricspaceswithapplicationstoorliczsobolevembeddings