Some s-numbers of embeddings of function spaces with weights of logarithmic type

被引：4

作者：

Gasiorowska, Alicja ^{[1
]}

Skrzypczak, Leszek ^{[1
]}

机构：

[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan, Poland

来源：

MATHEMATISCHE NACHRICHTEN | 2013年 / 286卷 / 07期

关键词：

Weighted function spaces; compact embeddings; Gelfand numbers; Kolmogorov numbers; Weyl numbers; distribution of eigenvalues; degenerate pseudodifferential operators; negative spectrum; ENTROPY NUMBERS; APPROXIMATION NUMBERS; BESOV-SPACES; WEYL NUMBERS; EIGENVALUE DISTRIBUTIONS; OPERATORS;

D O I：

10.1002/mana.201100086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we deal with compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type with weights of logarithmic growth near infinity. We obtain the exact estimates for the asymptotic behaviour of Gelfand, Kolmogorov and Weyl numbers of the embeddings. As an application we get eigenvalue estimates of some degenerate pseudodifferential operators of type. Finally we deal with the negative spectrum of operators H-gamma = A - gamma V for gamma -> infinity, where the potential V is a positive function and A is a positive elliptic pseudodifferential operator. We concentrate on the case when the Weyl numbers and Pietsch's inequality give us better estimates then entropy numbers and Carl's inequality. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：644 / 658

页数：15

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