English

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.

Keywords

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}
}
R2 v1 2026-06-28T16:06:00.150Z