## Abstract and Applied Analysis

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

Arman Karapetyan

#### 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 ${\prod }_{i=1}^{n}{(1-|{w}_{1}{|}^{2}-|{w}_{2}{|}^{2}-\cdots -|{w}_{i}{|}^{2})}^{{\alpha }_{i}}$, $w=({w}_{1},{w}_{2},\dots ,{w}_{n})\in {B}_{n}$. 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