Hausdorff operators on compact abelian groups

A. R. Mirotin

Mathematische Nachrichten, 2023, vol. 296, issue 9, 4108-4124

Abstract: Necessary and sufficient conditions are given for the boundedness of Hausdorff operators on the generalized Hardy spaces HEp(G)$H^p_E(G)$, real Hardy space HR1(G)$H^1_{\mathbb {R}}(G)$, BMO(G)$\text{BMO}(G)$, and BMOA(G)$\text{BMOA}(G)$ 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.

Date: 2023
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