Commuting relations for Hausdorff operators and Hilbert transforms on real Hardy spaces

Elijah Liflyand; Ferenc Móricz

doi:10.1023/a:1020867130612

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Acta Mathematica Hungarica

Volume/Issue:: Volume 97: Issue 1-2

Commuting relations for Hausdorff operators and Hilbert transforms on real Hardy spaces

Authors: Elijah Liflyand¹ and Ferenc Móricz²

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¹ Bar-Ilan University Department of Mathematics and Computer Science 52900 Ramat-Gan Israel 52900 Ramat-Gan Israel
² University of Szeged Bolyai Institute Aradi vértanúk tere 1 6720 Szeged Hungary Aradi vértanúk tere 1 6720 Szeged Hungary

DOI:: https://doi.org/10.1023/a:1020867130612

Page Count:: 133–143

Publication Date:: 01 Oct 2002

Online Publication Date:: 03 Nov 2004

Article Category:: Research Article

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Abstract

We consider Hausdorff operators generated by a function ϕ integrable in Lebesgue"s sense on either R or R², and acting on the real Hardy space H¹(R), or the product Hardy space H¹¹(RR), or one of the hybrid Hardy spaces H¹⁰(R²) and H⁰¹(R²), respectively. We give a necessary and sufficient condition in terms of ϕ that the Hausdorff operator generated by it commutes with the corresponding Hilbert transform.