A Generalized Hardy Operator on Rearrangement Invariant Spaces

Oscar Blasco*, Carolina Espinoza-Villalva

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages10
StatePublished - 2022

Publication series

NameTrends 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.


  • Boyd index
  • Hardy operator
  • Rearrangement invariant space


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