Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

作     者：Ricardo ABREU-BLAYA Juan BORY-REYES Fred BRACKX Hennie DE SCHEPPER Frank SOMMEN 

作者机构：Facultad de Informática y Matemática Universidad de Holguín Departamento de Matemática Universidad de Oriente Clifford Research Group Faculty of Engineering Ghent University Clifford Research Group Faculty of Sciences Ghent University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2012年第28卷第11期

页      面：2289-2300页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Hermitean Clifford analysis Hilbert transform fractal geometry 

摘      要：A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary F of a Jordan domain Ω in R2n, has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the HSlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the HSlder exponents, the diameter of F and a specific d-sum （d 〉 d） of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.