The korenblum maximum principle for some function spaces - Wee, JunJie (2019)
We study the Korenblum Maximum Principle on the weighted Fock space Fpα(C) and the weighted Bergman space Apα(D) under the gaussian weight e−pα2|z|2. We obtain explicit expressions for the upper bounds of Korenblum constants for the weighted Fock space Fpα(C), p ≥ 1 and α > 0. Then, we obtain upper bounds of such constants for the weighted Bergman space Apα(D), p ≥ 1 and α ≥ 0. We also show a failure of the Korenblum Maximum Principle for weighted Bergman space Apα(D), where 0 < p < 1, α > 0, thus bringing closure of the problem under weighted Bergman space Apα(D) where α > 0.