Abstract :
Let A2(D) be the Bergman space over the open unit diskD in the complex plane. Korenblum conjectured that there is an absolute
constant c ∈ (0, 1) such that whenever |f (z)| |g(z)| in the annulus c < |z| < 1, then f (z) g(z) . This conjecture had been
solved by Hayman [W.K. Hayman, On a conjecture of Korenblum, Analysis (Munich) 19 (1999) 195–205. [1]], but the constant c
in that paper is not optimal. Since then, there are many papers dealing with improving the upper and lower bounds for the best
constant c. For example, 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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