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Boundedness of integral operators on decreasing functions

Part of: General theory of linear operators Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  30 June 2015

María J. Carro  and
Carmen Ortiz-Caraballo
María J. Carro
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain (carro@ub.edu)
Carmen Ortiz-Caraballo
Affiliation:
Departamento de Matemáticas, Escuela Politécnica, Universidad de Extremadura, Avda. Universidad, s/n, 10003 Cáceres, Spain (carortiz@unex.es)
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Abstract

We continue the study of the boundedness of the operator

on the set of decreasing functions in Lp(w). This operator was first introduced by Braverman and Lai and also studied by Andersen, and although the weighted weak-type estimate was completely solved, the characterization of the weights w such that is bounded is still open for the case in which p > 1. The solution of this problem will have applications in the study of the boundedness on weighted Lorentz spaces of important operators in harmonic analysis.

Keywords

weak Lp-spacesHardy-Littlewood maximal operatorMuckenhoupt weights

MSC classification

Primary: 46B70: Interpolation between normed linear spaces
Secondary: 47A30: Norms (inequalities, more than one norm, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 4 , August 2015 , pp. 725 - 744
Copyright
Copyright © Royal Society of Edinburgh 2015 

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