Sharp embeddings of Besov spaces involving only logarithmic smoothness

被引：29

作者：

Caetano, Antonio M. ^{[1
]}

Gogatishvili, Amiran ^{[2
]}

Opic, Bohumir ^{[2
,3
]}

机构：

[1] Univ Aveiro, Dept Matemat, P-3810193 Aveiro, Portugal

[2] Acad Sci Czech Republic, Inst Math, CR-11567 Prague 1, Czech Republic

[3] Tech Univ Liberec, Dept Math & Didact Math, Liberec 46117, Halkova, Czech Republic

来源：

JOURNAL OF APPROXIMATION THEORY | 2008年 / 152卷 / 02期

关键词：

Besov spaces with generalized smoothness; Lorentz-Zygmund spaces; sharp embeddings; growth envelopes;

D O I：

10.1016/j.jat.2007.12.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use Kolyada's inequality and its converse form to prove sharp embeddings of Besov spaces B-p,r(0,beta) (involving the zero classical smoothness and a logarithmic smoothness with the exponent beta) into Lorentz-Zygmund spaces. We also determine growth envelopes of spaces B-p,r(0,beta). In distinction to the case when the classical smoothness is positive, we show that we cannot describe all embeddings in question in terms of growth envelopes. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：188 / 214

页数：27

共 18 条

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