Weighted Hardy and singular operators in Morrey spaces

被引：92
作者：
Samko, Natasha [1 ]
机构：
[1] Univ Algarve, Dept Matemat, P-8005139 Faro, Portugal
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 350卷 / 01期
关键词：
Morrey space; Singular operator; Hardy operator; Hardy-Littlewood maximal operator; Weighted estimate; INTEGRAL-OPERATORS; HOMOGENEOUS TYPE; FRACTIONAL INTEGRALS; RIESZ-POTENTIALS; MAXIMAL OPERATOR; INEQUALITIES; BOUNDEDNESS; CAMPANATO; INFINITY;
D O I：
10.1016/j.jmaa.2008.09.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the weighted boundedness of the Cauchy singular integral operator S-Gamma in Morrey spaces L-p,L-lambda '(Gamma) on Curves satisfying the arc-chord condition, for a class of "radial type" almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces L-p,L-lambda(0. e), e > 0. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves. (c) 2008 Elsevier Inc. All rights reserved.
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收藏
页码：56 / 72
页数：17
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