Commuting relations for Hausdorff operators and Hilbert transforms on real Hardy spaces |
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Authors: | Elijah Liflyand Ferenc Móricz |
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Affiliation: | (1) Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel;(2) Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary |
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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. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | hybrid Hardy spaces H10(R2) and H01(R2) commuting relation Fourier transform Hilbert transform real Hardy space H1(R) Hausdorff operator product Hardy space H11(R×R) Cesàro operator |
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