Holomorphic extension theorems in lipschitz domains of C2

Ricardo Abreu Blaya; Juan Bory Reyes; Dixan Peña Peña; Frank Sommen

doi:10.1007/s00006-008-0137-0

Holomorphic extension theorems in lipschitz domains of C²

Ricardo Abreu Blaya, Juan Bory Reyes, Dixan Peña Peña, Frank Sommen

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

2 Scopus citations

Abstract

The holomorphic functions of several complex variables are closely related to the continuously differentiable solutions f: R²ⁿ → C_n of the so-called isotonic system ∂_x1 + if̃∂_x2 = 0. The aim of this paper is to bring together these two areas which are intended as a good generalization of the classical one-dimensional complex analysis. In particular, it is of interest to study how far some classical holomorphic extension theorems can be stretched when the regularity of the boundary is reduced from C¹-smooth to Lipschitz. As an illustration, we give a complete viewpoint on simplified proofs of Kytmanov-Aronov-Aǐzenberg type theorems for the case n = 2.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Advances in Applied Clifford Algebras
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s00006-008-0137-0
State	Published - 2010
Externally published	Yes

Keywords

Clifford analysis
Isotonic functions
Sokhotski-plemelj formulae

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title = "Holomorphic extension theorems in lipschitz domains of C2",

abstract = "The holomorphic functions of several complex variables are closely related to the continuously differentiable solutions f: R2n → Cn of the so-called isotonic system ∂x1 + i{\~f}∂x2 = 0. The aim of this paper is to bring together these two areas which are intended as a good generalization of the classical one-dimensional complex analysis. In particular, it is of interest to study how far some classical holomorphic extension theorems can be stretched when the regularity of the boundary is reduced from C1-smooth to Lipschitz. As an illustration, we give a complete viewpoint on simplified proofs of Kytmanov-Aronov-Aǐzenberg type theorems for the case n = 2.",

keywords = "Clifford analysis, Isotonic functions, Sokhotski-plemelj formulae",

author = "Blaya, {Ricardo Abreu} and Reyes, {Juan Bory} and Pe{\~n}a, {Dixan Pe{\~n}a} and Frank Sommen",

note = "Funding Information: The first two authors wish to thank the IMPA, Rio de Janeiro, where the paper was written for the invitation and hospitality. They were partially supported by the CAPES-MES project 028/07. Dixan Pe{\~n}a Pe{\~n}a was supported by a Doctoral Grant of the Special Research Fund of Ghent University and Frank Sommen was supported by the FWO “Krediet aan Navorsers: 1.5.062.08”.",

year = "2010",

doi = "10.1007/s00006-008-0137-0",

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volume = "20",

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journal = "Advances in Applied Clifford Algebras",

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T1 - Holomorphic extension theorems in lipschitz domains of C2

AU - Blaya, Ricardo Abreu

AU - Reyes, Juan Bory

AU - Peña, Dixan Peña

AU - Sommen, Frank

N1 - Funding Information: The first two authors wish to thank the IMPA, Rio de Janeiro, where the paper was written for the invitation and hospitality. They were partially supported by the CAPES-MES project 028/07. Dixan Peña Peña was supported by a Doctoral Grant of the Special Research Fund of Ghent University and Frank Sommen was supported by the FWO “Krediet aan Navorsers: 1.5.062.08”.

PY - 2010

Y1 - 2010

N2 - The holomorphic functions of several complex variables are closely related to the continuously differentiable solutions f: R2n → Cn of the so-called isotonic system ∂x1 + if̃∂x2 = 0. The aim of this paper is to bring together these two areas which are intended as a good generalization of the classical one-dimensional complex analysis. In particular, it is of interest to study how far some classical holomorphic extension theorems can be stretched when the regularity of the boundary is reduced from C1-smooth to Lipschitz. As an illustration, we give a complete viewpoint on simplified proofs of Kytmanov-Aronov-Aǐzenberg type theorems for the case n = 2.

AB - The holomorphic functions of several complex variables are closely related to the continuously differentiable solutions f: R2n → Cn of the so-called isotonic system ∂x1 + if̃∂x2 = 0. The aim of this paper is to bring together these two areas which are intended as a good generalization of the classical one-dimensional complex analysis. In particular, it is of interest to study how far some classical holomorphic extension theorems can be stretched when the regularity of the boundary is reduced from C1-smooth to Lipschitz. As an illustration, we give a complete viewpoint on simplified proofs of Kytmanov-Aronov-Aǐzenberg type theorems for the case n = 2.

KW - Clifford analysis

KW - Isotonic functions

KW - Sokhotski-plemelj formulae

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DO - 10.1007/s00006-008-0137-0

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AN - SCOPUS:77952291685

SN - 0188-7009

VL - 20

SP - 1

EP - 12

JO - Advances in Applied Clifford Algebras

JF - Advances in Applied Clifford Algebras

IS - 1

ER -

Holomorphic extension theorems in lipschitz domains of C²

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