On weights which admit the reproducing kernel of Bergman type

On weights which admit the reproducing kernel of Bergman type

In this paper we consider (1) the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and (2) the kernels defined by such weights. It is verified that the weighted Bergman kernel has the analogous properties as the classical one....

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Main Author: Zbigniew Pasternak-Winiarski
Format: Article
Language:English
Published: Hindawi Limited 1992-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Bergman spaces
Bergman kernel
weighted Bergman function
admissible weights.
Online Access:http://dx.doi.org/10.1155/S0161171292000012
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spelling doaj-ef4723229966470fb61e68ae2a13b80c2020-11-25T02:17:27ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115111410.1155/S0161171292000012On weights which admit the reproducing kernel of Bergman typeZbigniew Pasternak-Winiarski0Institute of Mathematics, Technical University of Warsaw, Pl. Jedności Robotniczej 1, Warsaw 00-661, PolandIn this paper we consider (1) the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and (2) the kernels defined by such weights. It is verified that the weighted Bergman kernel has the analogous properties as the classical one. We prove several sufficient conditions and necessary and sufficient conditions for a weight to be an admissible weight. We give also an example of a weight which is not of this class. As a positive example we consider the weight μ(z)=(Imz)2 defined on the unit disk in ℂ.http://dx.doi.org/10.1155/S0161171292000012Bergman spacesBergman kernelweighted Bergman functionadmissible weights.
collection DOAJ
language English
format Article
sources DOAJ
author Zbigniew Pasternak-Winiarski
spellingShingle Zbigniew Pasternak-Winiarski
On weights which admit the reproducing kernel of Bergman type
International Journal of Mathematics and Mathematical Sciences
Bergman spaces
Bergman kernel
weighted Bergman function
admissible weights.
author_facet Zbigniew Pasternak-Winiarski
author_sort Zbigniew Pasternak-Winiarski
title On weights which admit the reproducing kernel of Bergman type
title_short On weights which admit the reproducing kernel of Bergman type
title_full On weights which admit the reproducing kernel of Bergman type
title_fullStr On weights which admit the reproducing kernel of Bergman type
title_full_unstemmed On weights which admit the reproducing kernel of Bergman type
title_sort on weights which admit the reproducing kernel of bergman type
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 1992-01-01
description In this paper we consider (1) the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and (2) the kernels defined by such weights. It is verified that the weighted Bergman kernel has the analogous properties as the classical one. We prove several sufficient conditions and necessary and sufficient conditions for a weight to be an admissible weight. We give also an example of a weight which is not of this class. As a positive example we consider the weight μ(z)=(Imz)2 defined on the unit disk in ℂ.
topic Bergman spaces
Bergman kernel
weighted Bergman function
admissible weights.
url http://dx.doi.org/10.1155/S0161171292000012
work_keys_str_mv AT zbigniewpasternakwiniarski onweightswhichadmitthereproducingkernelofbergmantype
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