Boundedness of integral operators on decreasing functions

María J. Carro; Carmen Ortiz-Caraballo

doi:10.1017/S0308210515000098

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

Show author details

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)

Article contents

Abstract

Rights & Permissions

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.