Sharp embeddings of Besov spaces with logarithmic smoothness
type: Item
instance of: scholarly article
title: Sharp embeddings of Besov spaces with logarithmic smoothness
zbMATH Open document ID: 1083.46018
author: Petr Gurka
author: Bohumír Opic
published in: Revista Matemática Complutense
publication date: 2005-07-13T00:00:00Z
full work available at URL: https://eudml.org/doc/44545
review text: The paper deals with generalized Besov spaces \(B^{\sigma, \alpha}_{p,r} ({\mathbb R}^n)\), where \(1\leq p,r \leq \infty\) refer to the integrability indices, \(\sigma >0\) stands for the usual (main) smoothness and \(\alpha\) indicates a logarithmic perturbation. The main aim is to study embeddings of type \[ B^{\sigma, \alpha}_{p,r} ({\mathbb R}^n) \hookrightarrow L_{q,s,\alpha} (\Omega), \] where \(\Omega\) is a bounded domain in \({\mathbb R}^n\) and \(L_{q,s,\alpha} (\Omega)\) stands for generalized Lorentz--Zygmund spaces. Necessary and sufficient conditions for these sharp embeddings are given in two relevant cases: (i) the subcritical case \(0 < \sigma < n/p\) (Theorem 2.1) and (ii) the critical case \(\sigma = n/p\) (Theorem 2.3). These results generalise corresponding earlier results by D.~D. Haroske, D.~E. Edmunds and the reviewer.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 2187070
zbMATH Keywords: generalized Besov spaces
zbMATH Keywords: Lorentz--Zygmund spaces
zbMATH Keywords: sharp embeddings
zbMATH Keywords: growth envelopes
MaRDI profile type: Publication
OpenAlex ID: W2138151113
DOI: 10.5209/REV_REMA.2005.V18.N1.16715
description: scientific article; zbMATH DE number 2187070