On the Forelli-Rudin construction and weighted Bergman projections
Ewa Ligocka (1989)
Studia Mathematica
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Ewa Ligocka (1989)
Studia Mathematica
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Frank Beatrous, Jacob Burbea
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CONTENTSIntroduction ..............................................................50. Preliminaries and notation....................................61. Hilbert spaces of holomorphic functions..............112. Some estimates ..................................................163. The space ............................................224. Norm estimates...................................................305. Sobolev norms....................................................356. Projections...
Henrik Delin (1998)
Annales de l'institut Fourier
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Weighted estimates are obtained for the canonical solution to the equation in , where is a pseudoconvex domain, and is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in . The weight is used to obtain a factor in the estimate of the kernel, where is the distance function in the Kähler metric given by the metric form .
Steven G. Krantz, Song-Ying Li (1995)
Annales de l'institut Fourier
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We study Hardy, Bergman, Bloch, and BMO spaces on convex domains of finite type in -dimensional complex space. Duals of these spaces are computed. The essential features of complex domains of finite type, that make these theorems possible, are isolated.
Elisabetta Barletta, Sorin Dragomir (1998)
Studia Mathematica
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We establish an inversion formula for the M. M. Djrbashian A. H. Karapetyan integral transform (cf. [6]) on the Siegel domain , . We build a family of Kähler metrics of constant holomorphic curvature whose potentials are the -Bergman kernels, α > -1, (in the sense of Z. Pasternak-Winiarski [20] of . We build an anti-holomorphic embedding of in the complex projective Hilbert space and study (in connection with work by A. Odzijewicz [18] the corresponding transition probability...
Ewa Ligocka (1998)
Studia Mathematica
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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.
Thomas Hansson (1999)
Annales de l'institut Fourier
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This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space . Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define with respect to a certain measure that degenerates near...
Zbigniew Pasternak-Winiarski, Paweł Wójcicki (2018)
Czechoslovak Mathematical Journal
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We study the limit behavior of weighted Bergman kernels on a sequence of domains in a complex space , and show that under some conditions on domains and weights, weighed Bergman kernels converge uniformly on compact sets. Then we give a weighted generalization of the theorem given by M. Skwarczyński (1980), highlighting some special property of the domains, on which the weighted Bergman kernels converge uniformly. Moreover, we show that convergence of weighted Bergman kernels implies...
Ewa Ligocka (1984)
Studia Mathematica
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