On a Maximum Principle for Bergman Spaces with Small Exponents

Abstract.

Let $A^{p}({\mathbb{D}})(0 < p < \infty)$ be the Bergman space over the open unit disk ${\mathbb{D}}$ in the complex plane. We know that Korenblum’s maximum principle holds when 1 ≤ p < ∞. In this note we prove that it is true for Bergman spaces with small exponents (0 < p < 1) under some supplementary conditions.