Korenblum’s Principle for Bergman Spaces with Radial Weights

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