Korenblum's principle for Bergman spaces with radial weights

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 $1\le p<\mathrm{\infty }$. 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 ${\mathrm{lim\hspace{0.17em}inf}}_{r\to 0^{+}}w(r)>0$, we show that the principle fails whenever $0<p<1$.