Hardy decomposition of higher order Lipschitz classes by polymonogenic functions
Complex Variables
2024-04-26 v1
Abstract
In this paper we find a decomposition of higher order Lipschitz functions into the traces of a polymonogenic function and solve a related Riemann-Hilbert problem. Our approach lies in using a cliffordian Cauchy-type operator, which behaves as an involution operator on higher order Lipschitz spaces. The result obtained is a multidimensional sharpened version of the Hardy decomposition of H\"older continuous functions on a simple closed curve in the complex plane.
Cite
@article{arxiv.2404.16447,
title = {Hardy decomposition of higher order Lipschitz classes by polymonogenic functions},
author = {Lianet De la Cruz Toranzo and Ricardo Abreu Blaya and Swanhild Bernstein},
journal= {arXiv preprint arXiv:2404.16447},
year = {2024}
}