Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛

We obtain weighted integral representations for spaces of functions holomorphic in the unit ball 𝐵𝑛 and belonging to area-integrable weighted 𝐿𝑝-classes with “anisotropic” weight function of the type ∏𝑛𝑖=1(1−|𝑤1|2−|𝑤2|2−⋯−|𝑤𝑖|2)𝛼𝑖, 𝑤=(𝑤1,𝑤2,…,𝑤𝑛)∈𝐵𝑛. The corresponding kernels of these representation...

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Main Author:	Arman Karapetyan
Format:	Article
Language:	English
Published:	Hindawi Limited 2010-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2010/354961

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spelling	doaj-840c104b55014814959c9422e203e4c92020-11-24T23:19:36ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/354961354961Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛Arman Karapetyan0Institute of Mathematics, National Academy of Sciences of Armenia, Marshal Bagramian Avenue 24 B, Yerevan 375019, ArmeniaWe obtain weighted integral representations for spaces of functions holomorphic in the unit ball 𝐵𝑛 and belonging to area-integrable weighted 𝐿𝑝-classes with “anisotropic” weight function of the type ∏𝑛𝑖=1(1−\|𝑤1\|2−\|𝑤2\|2−⋯−\|𝑤𝑖\|2)𝛼𝑖, 𝑤=(𝑤1,𝑤2,…,𝑤𝑛)∈𝐵𝑛. The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for 𝑛=2).http://dx.doi.org/10.1155/2010/354961
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Arman Karapetyan
spellingShingle	Arman Karapetyan Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛 Abstract and Applied Analysis
author_facet	Arman Karapetyan
author_sort	Arman Karapetyan
title	Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛
title_short	Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛
title_full	Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛
title_fullStr	Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛
title_full_unstemmed	Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛
title_sort	weighted anisotropic integral representations of holomorphic functions in the unit ball of 𝐶𝑛
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2010-01-01
description	We obtain weighted integral representations for spaces of functions holomorphic in the unit ball 𝐵𝑛 and belonging to area-integrable weighted 𝐿𝑝-classes with “anisotropic” weight function of the type ∏𝑛𝑖=1(1−\|𝑤1\|2−\|𝑤2\|2−⋯−\|𝑤𝑖\|2)𝛼𝑖, 𝑤=(𝑤1,𝑤2,…,𝑤𝑛)∈𝐵𝑛. The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for 𝑛=2).
url	http://dx.doi.org/10.1155/2010/354961
work_keys_str_mv	AT armankarapetyan weightedanisotropicintegralrepresentationsofholomorphicfunctionsintheunitballofcn
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Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of 𝐶𝑛

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