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On Korenblum's maximum principle

Author: Chunjie Wang
Journal: Proc. Amer. Math. Soc. 134 (2006), 2061-2066
MSC (2000): Primary 30C80, 30H05
Published electronically: January 5, 2006
MathSciNet review: 2215775
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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 $ \vert f(z)\vert\leq \vert g(z)\vert$ ( $ f,g\in A^2(\mathbb{D})$) in the annulus $ c<\vert z\vert<1$, then $ \Vert f\Vert _{A^2}\leq \Vert g\Vert _{A^2}$. In this paper we prove that Korenblum's maximum principle holds with $ c=0.25018$.

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Chunjie Wang
Affiliation: Department of Mathematics, Hebei University of Technology, Tianjin 300130, People’s Republic of China

Keywords: Bergman space, Korenblum's maximum principle, Fock space
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.