Hölder norm estimate for a Hilbert transform in Hermitean Clifford analysis

被引：0
作者：
Ricardo Abreu-Blaya
Juan Bory-Reyes
Fred Brackx
Hennie De Schepper
Frank Sommen
机构：
[1] Universidad de Holguín,Facultad de Informática y Matemática
[2] Universidad de Oriente,Departamento de Matemática
[3] Ghent University,Clifford Research Group, Faculty of Engineering
来源：
Acta Mathematica Sinica, English Series | 2012年 / 28卷
关键词：
Hermitean Clifford analysis; Hilbert transform; fractal geometry; 30G35;
D O I：
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中图分类号：
学科分类号：
摘要：
A Hilbert transform for Hölder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ 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 Hölder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hölder exponents, the diameter of Γ 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.
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页码：2289 / 2300
页数：11
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