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 → C<inf>n</inf> of the so-called isotonic system ∂<inf>x1</inf> + if̃∂<inf>x2</inf> = 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. © 2008 Birkhäuser Verlag Basel/Switzerland.

Año de publicación:

2010

Keywords:

• Sokhotski-plemelj formulae
• Clifford analysis
• Isotonic functions

Fuente:

scopus