Abstract and Applied Analysis

Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of C n

Arman Karapetyan

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Abstract

We obtain weighted integral representations for spaces of functions holomorphic in the unit ball B n and belonging to area-integrable weighted L p -classes with “anisotropic” weight function of the type i = 1 n ( 1 - | w 1 | 2 - | w 2 | 2 - - | w i | 2 ) α i , w = ( w 1 , w 2 , , w n ) B n . The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for n = 2 ).

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 354961, 23 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313170952

Digital Object Identifier
doi:10.1155/2010/354961

Mathematical Reviews number (MathSciNet)
MR2771235

Zentralblatt MATH identifier
1225.32008

Citation

Karapetyan, Arman. Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of $C^n$. Abstr. Appl. Anal. 2010 (2010), Article ID 354961, 23 pages. doi:10.1155/2010/354961. https://projecteuclid.org/euclid.aaa/1313170952


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