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On Korenblum's maximum principle

Authors:	Chunjie Wang

Institution:	Department of Mathematics, Hebei University of Technology, Tianjin 300130, People's Republic of China

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 .

Keywords:	Bergman space Korenblum's maximum principle Fock space

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