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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1992-01-01
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Online Access: | http://dx.doi.org/10.1155/S0161171292000012 |
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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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1724886296850071552 |