Korenblum’s Principle for Bergman Spaces with Radial Weights

Abstract

AbstractWe 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 ≤ 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 $$\liminf _{r\rightarrow 0^+} w(r)>0$$ lim inf r → 0 + w ( r ) > 0 , we show that the principle fails whenever $$0<p<1$$ 0 < p < 1 .