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arXiv · 2201.09328

Hausdorff Operators on Compact Abelian Groups

A. R. Mirotin
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Abstract

Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces $H^p_E(G)$, real Hardy space $H^1_{\mathbb{R}}(G)$, $BMO(G)$, and $BMOA(G)$ for compact Abelian group $G$. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on $G$ and examples are also considered.

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A. R. Mirotin. 2022-01-23. Hausdorff Operators on Compact Abelian Groups. https://arxiv.org/abs/2201.09328

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