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Behavior of holomorphic functions in complex tangential directions in a domain of finite type in Cn.

Sandrine Grellier (1992)

Publicacions Matemàtiques

Let Ω be a domain in Cn. It is known that a holomorphic function on Ω behaves better in complex tangential directions. When Ω is of finite type, the best possible improvement is quantified at each point by the distance to the boundary in the complex tangential directions (see the papers on the geometry of finite type domains of Catlin, Nagel-Stein and Wainger for precise definition). We show that this improvement is characteristic: for a holomorphic function, a regularity in complex tangential directions...

Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in ℂⁿ

Marco M. Peloso, Hercule Valencourt (2010)

Colloquium Mathematicae

We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces ℋ p , k ( ) , where is a smooth, bounded convex domain of finite type in ℂⁿ, by describing the approach regions for such functions. In particular, we extend a phenomenon first discovered by Nagel-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.

Boundary functions in L 2 H ( 𝔹 n )

Piotr Kot (2007)

Czechoslovak Mathematical Journal

We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball: For a function u which is lower semi-continuous on ∂ 𝔹 n we give necessary and sufficient conditions in order that there exists a holomorphic function f ∈ 𝕆 ( 𝔹 n ) such that u ( z ) = ∫ | λ | < 1 f ( λ z ) 2 d 𝔏 2 ( λ ) .

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