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

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Abstract

We consider Hausdorff operators generated by a function ϕ integrable in Lebesgue"s sense on either R or R 2, and acting on the real Hardy space H 1(R), or the product Hardy space H 11(R×R), or one of the hybrid Hardy spaces H 10(R 2) and H 01(R 2), 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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Elijah Liflyand

  2. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720, Szeged, Hungary

    Ferenc Móricz

Authors
  1. Elijah Liflyand
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  2. Ferenc Móricz
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Liflyand, E., Móricz, F. Commuting relations for Hausdorff operators and Hilbert transforms on real Hardy spaces. Acta Mathematica Hungarica 97, 133–143 (2002). https://doi.org/10.1023/A:1020867130612

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  • DOI: https://doi.org/10.1023/A:1020867130612

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