Korenblum’s principle for bergman spaces with radial weights

We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces Apw with arbitrary (non-negative and integrable) radial weights w in the case 1≤p<∞. 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 lim infr→0+w(r)>0, we show that the principle fails whenever 0<p<1.