Some results on Korenblumʹs maximum principle

Let A p ( D ) ( 1 ⩽ p < ∞ ) be the Bergman space over the open unit disk D in the complex plane. For p ⩾ 1 , let c p be the largest value of c for which Korenblumʹs maximum principle holds. In this paper we obtain a new lower bound on c p : c p ⩾ 0.23917 . We also improve the lower bound on c 2 up to 0.28185.