A Generalized Hardy Operator on Rearrangement Invariant Spaces

Oscar Blasco; Carolina Espinoza-Villalva

doi:10.1007/978-3-030-87502-2_32

A Generalized Hardy Operator on Rearrangement Invariant Spaces

Oscar Blasco^*, Carolina Espinoza-Villalva

^*Corresponding author for this work

Departamento de Matemáticas

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this paper we consider a weighted generalization of the Hardy operator acting on a rearrangement invariant function space. We give necessary and sufficient conditions for this linear operator to be bounded on a rearrangement invariant function space in terms of its upper Boyd index and the integrability of the norm of the dilation operator with respect to the considered weight.

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	315-324
Number of pages	10
DOIs	https://doi.org/10.1007/978-3-030-87502-2_32
State	Published - 2022

Publication series

Name	Trends in Mathematics
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Bibliographical note

Funding Information:
The first author is supported by Ministerio de Ciencia, Innovación y Universidades Project PGC2018-095366-B-I00 and the second author is supported by CONACYT, grant 711238.

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Boyd index
Hardy operator
Rearrangement invariant space

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10.1007/978-3-030-87502-2_32

Cite this

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AB - In this paper we consider a weighted generalization of the Hardy operator acting on a rearrangement invariant function space. We give necessary and sufficient conditions for this linear operator to be bounded on a rearrangement invariant function space in terms of its upper Boyd index and the integrability of the norm of the dilation operator with respect to the considered weight.

KW - Boyd index

KW - Hardy operator

KW - Rearrangement invariant space

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A Generalized Hardy Operator on Rearrangement Invariant Spaces

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