Hardy type inequalities in the category of hausdorff operators

Elijah Liflyand

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

Classical Hardy’s inequalities are concerned with the Hardy operator and its adjoint, the Bellman operator. Hausdorff operators in their various forms are natural generalizations of these two operators. In this paper, we try to adjust the scheme used by Bradley for Hardy’s inequalities with general weights to the Hausdorff setting. It is not surprising that the obtained necessary conditions differ from the sufficient conditions as well as that both depend not only on weights but also on the kernel that generate the Hausdorff operator. For the Hardy and Bellman operators, the obtained necessary and sufficient conditions coincide and reduce to the classical ones.

Original languageEnglish
Title of host publicationModern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions
EditorsAlexey Karapetyants, Vladislav Kravchenko, Elijah Liflyand
PublisherSpringer New York LLC
Pages81-91
Number of pages11
ISBN (Print)9783030267476
DOIs
StatePublished - 2019
EventInternational Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018 - Rostov-on-Don, Russian Federation
Duration: 22 Apr 201827 Apr 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume291
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018
Country/TerritoryRussian Federation
CityRostov-on-Don
Period22/04/1827/04/18

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Keywords

  • Hardy inequality
  • Hausdorff operator

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