Hardy decomposition of first order Lipschitz functions by Clifford algebra-valued harmonic functions

被引：0

作者：

Toranzo, Lianet De la Cruz ^{[1
]}

Blaya, Ricardo Abreu ^{[2
,3
]}

Bernstein, Swanhild ^{[1
]}

机构：

[1] TU Bergakademie Freiberg, Inst Appl Anal, Freiberg, Germany

[2] Univ Autonoma Guerrero, Fac Matemat, Chilpancingo, Mexico

[3] Univ UTE, Quito, Ecuador

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 536卷 / 01期

关键词：

Higher order Lipschitz functions; Clifford algebras; Bimonogenic functions; Singular integral operator; Hardy decomposition; Riemann problem;

D O I：

10.1016/j.jmaa.2024.128242

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we solve the problem on finding a sectionally Clifford algebra-valued harmonic function, zero at infinity and satisfying certain boundary value condition related to higher order Lipschitz functions. Our main tool are the Hardy projections related to a singular integral operator arising in bimonogenic function theory, which turns out to be an involution operator on the first order Lipschitz classes. Our result generalizes the classical Hardy decomposition of Holder continuous functions on a simple closed curve in the complex plane. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

引用

页数：13

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