The Bergman kernel on certain weakly pseudoconvex domains

1995 ◽  
Vol 220 (1) ◽  
pp. 1-9
Author(s):  
Nicholas Watts Gebelt
Keyword(s):  
Bergman Kernel ◽  
Pseudoconvex Domains ◽  
Weakly Pseudoconvex

scholarly journals On some extremal problems in Bergman spaces in weakly pseudoconvex domains

2018 ◽  
Vol 26 (2) ◽  
pp. 83-97
Author(s):  
Romi F. Shamoyan ◽  
Olivera R. Mihić
Keyword(s):  
Distance Function ◽  
Bergman Kernel ◽  
Additional Condition ◽  
Bergman Spaces ◽  
Representation Formula ◽  
Extremal Problems ◽  
Bergman Projection ◽  
Pseudoconvex Domains ◽  
Weakly Pseudoconvex

AbstractWe consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂn based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces $A_\alpha ^p$ in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.

scholarly journals The growth of the bergman kernel on pseudoconvex domains of homogeneous finite diagonal type

1992 ◽  
Vol 126 ◽  
pp. 1-24 ◽  
Author(s):  
Gregor Herbort
Keyword(s):  
Bergman Kernel ◽  
Sharp Estimate ◽  
Pseudoconvex Domains ◽  
Invariant Metrics ◽  
Weakly Pseudoconvex

In this article we continue the investigations on invariant metrics on a certain class of weakly pseudoconvex domains which we began in [H 1]. While in that paper the differential metrics of Caratheodory and Kobayashi were estimated precisely, the present paper contains a sharp estimate of the singularity of the Bergman kernel and metric on domains belonging to that class.

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