On Korenblum's maximum principle

Let A(2)( D) be the Bergman space over the open unit disk D in the complex plane. Korenblum's maximum principle states that there is an absolute constant c is an element of ( 0, 1), such that whenever vertical bar f( z) vertical bar <= vertical bar g( z) vertical bar ( f, g is an element of A(2)( D)) in the annulus c < vertical bar z vertical bar < 1, then parallel to f parallel to (A2) <= parallel to g parallel to (A2). In this paper we prove that Korenblum's maximum principle holds with c = 0.25018.