Hardy type inequalities in the category of hausdorff operators

Elijah Liflyand

doi:10.1007/978-3-030-26748-3_6

Hardy type inequalities in the category of hausdorff operators

Elijah Liflyand

Department of Mathematics

People's Friendship University of Russia

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

10 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 language	English
Title of host publication	Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions
Editors	Alexey Karapetyants, Vladislav Kravchenko, Elijah Liflyand
Publisher	Springer New York LLC
Pages	81-91
Number of pages	11
ISBN (Print)	9783030267476
DOIs	https://doi.org/10.1007/978-3-030-26748-3_6
State	Published - 2019
Event	International 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 2018 → 27 Apr 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	291
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018
Country/Territory	Russian Federation
City	Rostov-on-Don
Period	22/04/18 → 27/04/18

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Keywords

Hardy inequality
Hausdorff operator

Access to Document

10.1007/978-3-030-26748-3_6

Cite this

Liflyand, E. (2019). Hardy type inequalities in the category of hausdorff operators. In A. Karapetyants, V. Kravchenko, & E. Liflyand (Eds.), Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions (pp. 81-91). (Springer Proceedings in Mathematics and Statistics; Vol. 291). Springer New York LLC. https://doi.org/10.1007/978-3-030-26748-3_6

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Liflyand, E 2019, Hardy type inequalities in the category of hausdorff operators. in A Karapetyants, V Kravchenko & E Liflyand (eds), Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions. Springer Proceedings in Mathematics and Statistics, vol. 291, Springer New York LLC, pp. 81-91, International Scientific Conference of Modern Methods and Problems of Operator Theory and Harmonic Analysis and Their Applications, OTHA 2018, Rostov-on-Don, Russian Federation, 22/04/18. https://doi.org/10.1007/978-3-030-26748-3_6

Hardy type inequalities in the category of hausdorff operators. / Liflyand, Elijah.
Modern Methods in Operator Theory and Harmonic Analysis - OTHA 2018, Revised and Extended Contributions. ed. / Alexey Karapetyants; Vladislav Kravchenko; Elijah Liflyand. Springer New York LLC, 2019. p. 81-91 (Springer Proceedings in Mathematics and Statistics; Vol. 291).

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

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Hardy type inequalities in the category of hausdorff operators

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