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Application of a Riesz-type formula to weighted Bergman spaces


Author: Ali Abkar
Journal: Proc. Amer. Math. Soc. 131 (2003), 155-164
MSC (2000): Primary 31A30; Secondary 30E10, 30H05, 46E10
DOI: https://doi.org/10.1090/S0002-9939-02-06491-2
Published electronically: May 13, 2002
MathSciNet review: 1929035
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Abstract: Let $\mathbb{D}$ denote the unit disk in the complex plane. We consider a class of superbiharmonic weight functions $w\colon \mathbb{D} \to \mathbb{R}^+$ whose growth are subject to the condition $0\le w(z)\le C(1-\vert z\vert)$ for some constant $C$. We first establish a Reisz-type representation formula for $w$, and then use this formula to prove that the polynomials are dense in the weighted Bergman space with weight $w$.


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Additional Information

Ali Abkar
Affiliation: Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Qazvin 34194, Iran
Address at time of publication: Department of Mathematics, Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-1795, Tehran, Iran
Email: abkar@ipm.ir

DOI: https://doi.org/10.1090/S0002-9939-02-06491-2
Received by editor(s): August 16, 2001
Published electronically: May 13, 2002
Additional Notes: This research was supported in part by a grant from the Institute for Theoretical Physics and Mathematics (IPM), Tehran, Iran.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2002 American Mathematical Society

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