Displaying similar documents to “On Hardy spaces in complex ellipsoids”

C k -estimates for the ∂ ¯ -equation on concave domains of finite type

William Alexandre (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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C k estimates for convex domains of finite type in ℂ n are known from [] for k = 0 and from [] for k > 0 . We want to show the same result for concave domains of finite type. As in the case of strictly pseudoconvex domain, we fit the method used in the convex case to the concave one by switching z and ζ in the integral kernel of the operator used in the convex case. However the kernel will not have the same behavior on the boundary as in the Diederich-Fischer-Fornæss-Alexandre work....

Weighted Bergman projections and tangential area integrals

William Cohn (1993)

Studia Mathematica

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Let Ω be a bounded strictly pseudoconvex domain in ℂ n . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection P s f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space H k p ( ∂ Ω ) .

Henkin-Ramirez formulas with weight factors

B. Berndtsson, Mats Andersson (1982)

Annales de l'institut Fourier

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We construct a generalization of the Henkin-Ramírez (or Cauchy-Leray) kernels for the ∂ ‾ -equation. The generalization consists in multiplication by a weight factor and addition of suitable lower order terms, and is found via a representation as an “oscillating integral”. As special cases we consider weights which behave like a power of the distance to the boundary, like exp- ϕ with ϕ convex, and weights of polynomial decrease in C n . We also briefly consider kernels with singularities on...

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

Sandrine Grellier (1992)

Publicacions Matemàtiques

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Let Ω be a domain in C. 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...