Hardy decomposition of higher order Lipschitz classes by polymonogenic functions

2024/04/25 by Lianet De la Cruz Toranzo, Toranzo, Lianet De la Cruz, Ricardo Abreu Blaya +3
Mathematics · #30G35 #31B10 #47A05 #47B38 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2404.16447

openalex publication_date 2024/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Hölder continuous functions on a simple closed curve in the complex plane.

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