English

Hausdorff Operators on Compact Abelian Groups

Functional Analysis 2022-01-25 v1

Abstract

Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces HEp(G)H^p_E(G), real Hardy space HR1(G)H^1_{\mathbb{R}}(G), BMO(G)BMO(G), and BMOA(G)BMOA(G) for compact Abelian group GG. 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 GG and examples are also considered.

Keywords

Cite

@article{arxiv.2201.09328,
  title  = {Hausdorff Operators on Compact Abelian Groups},
  author = {A. R. Mirotin},
  journal= {arXiv preprint arXiv:2201.09328},
  year   = {2022}
}
R2 v1 2026-06-24T08:59:15.428Z