Korenblum’s Principle for Bergman Spaces with Radial Weights

Abstract

We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces \(A^p_w\) with arbitrary (non-negative and integrable) radial weights w in the case \(1\le p<\infty \). We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption \(\liminf _{r\rightarrow 0^+} w(r)>0\), we show that the principle fails whenever \(0<p<1\).