On Korenblum's maximum principle

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 $c=0.25018$.