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

Elijah Liflyand; Ferenc Móricz

doi:10.1023/a:1020867130612

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

Elijah Liflyand
, Ferenc Móricz

Department of Mathematics

University of Szeged

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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(R × R), 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.

Original language	English
Pages (from-to)	133-143
Number of pages	11
Journal	Acta Mathematica Hungarica
Volume	97
Issue number	1-2
DOIs	https://doi.org/10.1023/a:1020867130612
State	Published - Oct 2002

Keywords

Cesàro operator
Fourier transform
Hausdorff operator
Hilbert transform
Hybrid Hardy spaces H (R) and H (R)
Product Hardy space H (R × R)
Real Hardy space H (R)

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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(R × R), 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.",

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AU - Móricz, Ferenc

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AB - 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(R × R), 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.

KW - Cesàro operator

KW - Fourier transform

KW - Hausdorff operator

KW - Hilbert transform

KW - Hybrid Hardy spaces H (R) and H (R)

KW - Product Hardy space H (R × R)

KW - Real Hardy space H (R)

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SN - 0236-5294

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EP - 143

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1-2

ER -

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

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