scholarly journals BOUNDARY BEHAVIOR OF HOLOMORPHIC DISCS IN CONVEX FINITE TYPE DOMAINS

2015 ◽  
Vol 31 (3) ◽  
pp. 351-356
Author(s):  
Kang-Hyurk Lee
Keyword(s):  
Finite Type ◽  
Boundary Behavior ◽  
Finite Type Domains ◽  
Holomorphic Discs

scholarly journals EXTENSION AND RESTRICTION FOR BERGMAN SCALE OF SPACES AND ONE-DIMENSIONAL SUBVARIETIES ON CONVEX FINITE TYPE DOMAINS

2016 ◽  
Vol 221 (1) ◽  
pp. 165-183
Author(s):  
M. JASICZAK
Keyword(s):  
Finite Type ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Extension Problem ◽  
One Dimensional ◽  
Finite Type Domains

We prove that the extension problem from one-dimensional subvarieties with values in Bergman space $H^{1}(D)$ on convex finite type domains can be solved by means of appropriate measures. We obtain also almost optimal results concerning the extension problem for other Bergman spaces and one-dimensional varieties.

scholarly journals Boundary behavior of functions holomorphic in domains of finite type

1981 ◽  
Vol 78 (11) ◽  
pp. 6596-6599 ◽  
Author(s):  
A. Nagel ◽  
E. M. Stein ◽  
S. Wainger
Keyword(s):  
Finite Type ◽  
Boundary Behavior

ON DISCONTINUITY OF THE BERGMAN KERNEL FUNCTION

1999 ◽  
Vol 10 (07) ◽  
pp. 825-832
Author(s):  
KLAS DIEDERICH ◽  
GREGOR HERBORT
Keyword(s):  
Finite Type ◽  
Kernel Function ◽  
Real Line ◽  
Bergman Kernel ◽  
Pseudoconvex Domain ◽  
Convex Domains ◽  
Bergman Kernel Function ◽  
Finite Type Domains

Let [Formula: see text] be a Ck-smoothly (with k≥1) bounded pseudoconvex domain and [Formula: see text] denote its Bergman kernel function. In this article the question is investigated, whether the function [Formula: see text] is continuous up to the boundary in the topology of the extended real line [Formula: see text]. We give two counterexamples: one in the class of finite type domains with k = ∞ and one in the class of convex domains with k = 1.

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