Application of a Riesz-type formula to weighted Bergman spaces
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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 $0\le w(z)\le C(1-|z|)$ 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 $w$.References
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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
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1929035