English

On a general concept of a Hausdorff-type operator

Functional Analysis 2024-06-18 v2

Abstract

A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration in LpL^p and in the atomic Hardy space H1H^1, and their regularity property is investigated. Examples are considered. The author hopes that this approach will allow one to unify the study of a lot of extensions and analogs of the classical Hausdorff operator.

Keywords

Cite

@article{arxiv.2308.02388,
  title  = {On a general concept of a Hausdorff-type operator},
  author = {A. R. Mirotin},
  journal= {arXiv preprint arXiv:2308.02388},
  year   = {2024}
}