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arXiv · 0706.1099

A slight improvement to Korenblum's constant

Chun-Yen Shen
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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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Chun-Yen Shen. 2007-06-07. A slight improvement to Korenblum's constant. https://doi.org/10.1016/j.jmaa.2007.04.015

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