On limiting embeddings of Besov spaces

V. I. Kolyada; A. K. Lerner

doi:10.4064/sm171-1-1

On limiting embeddings of Besov spaces

V. I. Kolyada, A. K. Lerner

Department of Mathematics

Karlstad University

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We investigate the classical embedding B_p,θ^s ⊂ B_q,θ^s-n(1/p-1/q). The sharp asymptotic behaviour as s → 1 of the operator norm of this embedding is found. In particular, our result yields a refinement of the Bourgain, Brezis and Mironescu theorem concerning an analogous problem for the Sobolev-type embedding. We also give a different, elementary proof of the latter theorem.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Studia Mathematica
Volume	171
Issue number	1
DOIs	https://doi.org/10.4064/sm171-1-1
State	Published - 2005

Keywords

Besov space
Embedding theorem
Modulus of continuity
Rearrangement estimate

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10.4064/sm171-1-1

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On limiting embeddings of Besov spaces

Abstract

Keywords

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