On Korenblum’s maximum principle
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- by Chunjie Wang PDF
- Proc. Amer. Math. Soc. 134 (2006), 2061-2066 Request permission
Abstract:
Let $A^2(\mathbb {D})$ be the Bergman space over the open unit disk $\mathbb {D}$ in the complex plane. Korenblum’s maximum principle states that there is an absolute constant $c\in (0,1)$, such that whenever $|f(z)|\leq |g(z)|$ ($f,g\in A^2(\mathbb {D})$) in the annulus $c<|z|<1$, then $\|f\|_{A^2}\leq \|g\|_{A^2}$. In this paper we prove that Korenblum’s maximum principle holds with $c=0.25018$.References
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Additional Information
- Chunjie Wang
- Affiliation: Department of Mathematics, Hebei University of Technology, Tianjin 300130, People’s Republic of China
- Email: wcj498@eyou.com
- Received by editor(s): December 10, 2004
- Received by editor(s) in revised form: February 14, 2005
- Published electronically: January 5, 2006
- Additional Notes: This work was supported by NNSF of China No. 10401002 and the Doctoral Foundation of Hebei University of Technology.
- Communicated by: Joseph A. Ball
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2061-2066
- MSC (2000): Primary 30C80, 30H05
- DOI: https://doi.org/10.1090/S0002-9939-06-08311-0
- MathSciNet review: 2215775