Weighted singular integral operators in Clifford analysis

Juan Bory Reyes; Ricardo Abreu Blaya

doi:10.1002/mma.380

Weighted singular integral operators in Clifford analysis

Juan Bory Reyes, Ricardo Abreu Blaya

Research output: Contribution to journal › Article › peer-review

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Abstract

We consider the Cauchy-type integral and singular integral operator having a weighted Cauchy kernel, both over a domain bounded by an n-dimensional surface in ℝⁿ⁺¹, n≥2. The aim of this paper is to study the behaviour of the weighted Cauchy singular integral operators near the integration boundary as well as to establish the basic relation among them. In certain sense, this approach has the advantage of being better related with boundary value problems than what is concerned in the setting of smooth surfaces.

Original language	English
Pages (from-to)	1429-1440
Number of pages	12
Journal	Mathematical Methods in the Applied Sciences
Volume	25
Issue number	16-18
DOIs	https://doi.org/10.1002/mma.380
State	Published - Nov 2002
Externally published	Yes

Keywords

Cauchy-type integral
Clifford analysis
Hausdorff measure

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10.1002/mma.380

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abstract = "We consider the Cauchy-type integral and singular integral operator having a weighted Cauchy kernel, both over a domain bounded by an n-dimensional surface in ℝn+1, n≥2. The aim of this paper is to study the behaviour of the weighted Cauchy singular integral operators near the integration boundary as well as to establish the basic relation among them. In certain sense, this approach has the advantage of being better related with boundary value problems than what is concerned in the setting of smooth surfaces.",

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AB - We consider the Cauchy-type integral and singular integral operator having a weighted Cauchy kernel, both over a domain bounded by an n-dimensional surface in ℝn+1, n≥2. The aim of this paper is to study the behaviour of the weighted Cauchy singular integral operators near the integration boundary as well as to establish the basic relation among them. In certain sense, this approach has the advantage of being better related with boundary value problems than what is concerned in the setting of smooth surfaces.

KW - Cauchy-type integral

KW - Clifford analysis

KW - Hausdorff measure

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ER -

Weighted singular integral operators in Clifford analysis

Abstract

Keywords

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