Dual of the space of holomorphic functions with continuous boundary values on a strictly pseudo-convex domain in ? n

1989 ◽  
Vol 284 (4) ◽  
pp. 537-562 ◽  
Author(s):  
Tosiaki Kori
Keyword(s):  
Convex Domain ◽  
Holomorphic Functions ◽  
Boundary Values ◽  
Pseudo Convex Domain ◽  
Pseudo Convex ◽  
Continuous Boundary

scholarly journals Sobolev and Lipschitz estimates for weighted Bergman projections

1997 ◽  
Vol 147 ◽  
pp. 147-178 ◽  
Author(s):  
Der-Chen Chang ◽  
Bao Qin Li
Keyword(s):  
Finite Type ◽  
Convex Domain ◽  
Functional Calculus ◽  
Smooth Boundary ◽  
Lipschitz Estimates ◽  
Pseudo Convex Domain ◽  
Pseudo Convex ◽  
Bergman Projections ◽  
Distance To The Boundary

AbstractLet Ω be a bounded, decoupled pseudo-convex domain of finite type in ℂn with smooth boundary. In this paper, we generalize results of Bonami-Grellier [BG] and Bonami-Chang-Grellier [BCG] to study weighted Bergman projections for weights which are a power of the distance to the boundary. We define a class of operators of Bergman type for which we develop a functional calculus. Then we may obtain Sobolev and Lipschitz estimates, both of isotropic and anisotropic type, for these projections.

Continuous Boundary Values of Holomorphic Functions on Kähler Domains

1976 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
Barnet M. Weinstock
Keyword(s):  
Potential Theory ◽  
Holomorphic Functions ◽  
Continuous Functions ◽  
Beltrami Operator ◽  
Compact Domain ◽  
Boundary Values ◽  
Codimension One ◽  
Continuous Boundary ◽  
Holomorphic Extensions ◽  
Real Codimension

LetMbe a complex manifold of dimensionnwhich admits a Kähler metric, and letDbe a relatively compact domain onMwhose boundaryBis a C ∞ submanifold ofMof real codimension one. The object of this paper is to use the potential theory associated with the Laplace-Beltrami operator onMto characterize the continuous functions onBwhich have holomorphic extensions toD.

A pseudo-convex domain not admitting a holomorphic support function

1973 ◽  
Vol 201 (4) ◽  
pp. 265-268 ◽  
Author(s):  
J. J. Kohn ◽  
L. Nirenberg
Keyword(s):  
Convex Domain ◽  
Support Function ◽  
Pseudo Convex Domain ◽  
Pseudo Convex

scholarly journals Bounded and Almost Periodic Ultradistributions as Boundary Values of Holomorphic Functions

2003 ◽  
Vol 33 (4) ◽  
pp. 1295-1311
Author(s):  
C. Fernández ◽  
A. Galbis ◽  
M.C. Gómez-Collado
Keyword(s):  
Holomorphic Functions ◽  
Almost Periodic ◽  
Boundary Values
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