Korenblum's principle for Bergman spaces with radial weights

Abstract

We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces $A_w^p$ 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 ${\mathrm{liminf}}_{r\to 0^{+}}w(r)>0$, we show that the principle fails whenever $0<p<1$.

In this version some minor misprints and language issues have been corrected. Also, the addresses and the dedicatory have been updated