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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