Hausdorff operators on compact abelian groups. (English) Zbl 07750706
Summary: Necessary and sufficient conditions are given for the boundedness of Hausdorff operators on the generalized Hardy spaces \(H^p_E(G)\), real Hardy space \(H^1_{\mathbb{R}}(G)\), \(\text{BMO}(G)\), and \(\text{BMOA}(G)\) 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.
© 2023 Wiley-VCH GmbH.
© 2023 Wiley-VCH GmbH.
MSC:
| 47B90 | Operator theory and harmonic analysis |
| 47B38 | Linear operators on function spaces (general) |
| 30B50 | Dirichlet series, exponential series and other series in one complex variable |
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