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

By Evgeniy Pustylnik

Abstract

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

Topics: Mathematics, QA1-939
Publisher: Hindawi Publishing Corporation
Year: 2005
DOI identifier: 10.1155/2005
OAI identifier: oai:doaj.org/article:28075a429d5c4ebc8dfc1f4a0500a22c
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