Korenblum maximum principle in mixed norm spaces

Abstract

It is well known that the Korenblum maximum principle holds in Bergman spaces A p if and only if p≥ 1. In this note, we improve this result by proving that the Korenblum maximum principle holds in mixed norm spaces H p,q,α when 1 ≤ p≤ q< ∞ and does not hold when 0 < q< 1. As an immediate consequence, we obtain that the Korenblum maximum principle holds in weighted Bergman spaces Aγp if and only if p≥ 1.