Regularity of the Bergman Projection in Weakly Pseudoconvex Domains.
Steven R. Bell, Harold P. Boas (1981)
Mathematische Annalen
David E. Barrett (1981)
Mathematische Annalen
Putinar, Gabriela, Putinar, Mihai (2006)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Qiannan Zhang, Huan Yang (2023)
Czechoslovak Mathematical Journal
In this paper we study the balanced metrics on some Hartogs triangles of exponent , i.e., equipped with a natural Kähler form with where , , depending on parameters. The purpose of this paper is threefold. First, we compute the explicit expression for the weighted Bergman kernel function for and we prove that is balanced if and only if and is an integer, are integers such that for all , and . Second, we prove that is Kähler-Einstein if and only if , where is a nonzero...
Ewa Ligocka (1998)
Studia Mathematica
We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be -smoothly extended to the boundary.
D. R. Georgijević (1986)
Matematički Vesnik
Keiko Fujita (2007)
Annales Polonici Mathematici
We consider holomorphic functions and complex harmonic functions on some balls, including the complex Euclidean ball, the Lie ball and the dual Lie ball. After reviewing some results on Bergman kernels and harmonic Bergman kernels for these balls, we consider harmonic continuation of complex harmonic functions on these balls by using harmonic Bergman kernels. We also study Szegő kernels and harmonic Szegő kernels for these balls.
David Békollé, Anatole Temgoua Kagou (1995)
Studia Mathematica
On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space .
G.M. Henkin, P.L. Polyakov (1990)
Mathematische Annalen
Mikael Passare (1988)
Mathematica Scandinavica
Jean-Pierre Ramis, Gabriel Ruget (1974)
Inventiones mathematicae
Driss Essouabri (1997)
Annales de l'institut Fourier
Soit un polynôme. On appelle série de Dirichlet associée à la fonction : . Dans cet article nous étudions l’existence et les propriétés du prolongement méromorphe d’une telle série sous l’hypothèse qu’il existe tel que : i) quand et et ii) où . Cette hypothèse est probablement optimale et en tout cas contient strictement toutes les classes de polynômes déjà traitées antérieurement. Sous cette hypothèse nos principaux résultats sont : l’existence du prolongement méromorphe au plan...
Harold P. Boas, Mei-Chi Shaw (1986)
Mathematische Annalen
Harold P. Boas, Emil J. Straube (1991)
Mathematische Zeitschrift
Gerd Schmalz (1989)
Mathematische Zeitschrift
Klaus Peters (1991)
Mathematische Annalen
Min Ku, Uwe Kähler, Paula Cerejeiras (2012)
Archivum Mathematicum
In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to the polynomially generalized Bers–Vekua equation with variable coefficients. Finally, we present the structure...
Jean-Pierre Rosay (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
I. Ramadanov (1983)
Banach Center Publications
Alessandro Perotti (2000)
Publicacions Matemàtiques
In this paper we investigate some applications of the trace condition for pluriharmonic functions on a smooth, bounded domain in Cn. This condition, related to the normal component on ∂D of the ∂-operator, permits us to study the Neumann problem for pluriharmonic functions and the ∂-problem for (0,1)-forms on D with solutions having assigned real part on the boundary.