Singular integral operators with fixed singularities on weighted Lebesgue spaces

被引：13

作者：

Karlovich, YI ^{[1
]}

de Arellano, ER ^{[1
]}

机构：

[1] IPN, CINVESTAV, Dept Matemat, Mexico City 07000, DF, Mexico

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2004年 / 48卷 / 03期

关键词：

singular integral operators; fixed singularities; Lebesgue spaces; Muckenhoupt weights; Banach algebras; symbols; Fredholm theory;

D O I：

10.1007/s00020-001-1182-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is devoted to study of singular integral operators with fixed singularities at endpoints of contours on weighted Lebesgue spaces with general Muckenhoupt weights. Compactness of certain integral operators with fixed singularities is established. The membership of singular integral operators with fixed singularities to Banach algebras of singular integral operators on weighted Lebesgue spaces with slowly oscillating Muckenhoupt weights is proved on the basis of Balakrishnan's formula from the theory of strongly continuous semi-groups of closed linear operators. Symbol calculus for such operators, Fredholm criteria and index formulas are obtained.

引用

页码：331 / 363

页数：33

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