Korenblum’s Principle for Bergman Spaces with Radial Weights

We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces \(A^p_w\) $A_w^p$ with arbitrary (non-negative and integrable) radial weights w in the case \(1\le p<\infty \) $1\le p<\infty$ . 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 \(\liminf _{r\rightarrow 0^+} w(r)>0\) ${lim\; inf}_{r\to 0^{+}}w(r)>0$ , we show that the principle fails whenever \(0<p<1\) $0<p<1$ .