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arXiv · 2308.02388

On a general concept of a Hausdorff-type operator

A. R. Mirotin
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Abstract

A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration in $L^p$ and in the atomic Hardy space $H^1$, and their regularity property is investigated. Examples are considered. The author hopes that this approach will allow one to unify the study of a lot of extensions and analogs of the classical Hausdorff operator.

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A. R. Mirotin. 2023-08-04. On a general concept of a Hausdorff-type operator. https://arxiv.org/abs/2308.02388

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