A slight improvement to Korenblum's constant

Abstract

Let $A^2(D)$ be the Bergman space over the open unit disk $D$ in the complex plane. Korenblum conjectured that there is an absolute constant $c\in (0,1)$ such that whenever $|f(z)|\le |g(z)|$ in the annulus $c<|z|<1$ then $||f(z)||\le ||g(z)||$.In 2004 C.Wang gave an upper bound on $c$,that is, $c<0.67795$, and in 2006 A.Schuster gave a lower bound ,$c>0.21$ .In this paper we slightly improve the upper bound for $c$.

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• Errata and Addenda to Mathematical Constants