Weighted hardy and singular operators in morrey spaces

• Autor(a) principal: Samko, Natasha
• Data de Publicação: 2009
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.1/11307
• topic: Integral-operators; Homogeneous type; Fractional integrals; Riesz-potentials; Maximal operator; Inequalities; Boundedness; Campanato; Infinity

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.