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 , real Hardy space , , and for compact Abelian group . 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 and examples are also considered.
Cite
@article{arxiv.2201.09328,
title = {Hausdorff Operators on Compact Abelian Groups},
author = {A. R. Mirotin},
journal= {arXiv preprint arXiv:2201.09328},
year = {2022}
}