Polyanalytic Hardy decomposition of higher order Lipschitz functions
Complex Variables
2023-02-09 v1 Classical Analysis and ODEs
Abstract
This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve into a sum of two polyanalytic functions in each open domain defined by . Our basic tools are the Hardy projections related to a singular integral operator arising in polyanalytic function theory, which, as it is proved here, represents an involution operator on the higher order Lipschitz classes. Our result generalizes the classical Hardy decomposition of Holder continuous functions on the boundary of a domain.
Cite
@article{arxiv.2005.03816,
title = {Polyanalytic Hardy decomposition of higher order Lipschitz functions},
author = {Ricardo Abreu Blaya and Lianet De la Cruz Toranzo},
journal= {arXiv preprint arXiv:2005.03816},
year = {2023}
}