Korenblum constants for some function spaces

JunJie, Wee; Khoi, Le

doi:10.1090/proc/14778

Korenblum constants for some function spaces
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by Wee JunJie and Le Hai Khoi PDF

Proc. Amer. Math. Soc. 148 (2020), 1175-1185 Request permission

Abstract:

We study the Korenblum Maximum Principle on the weighted Fock spaces and the weighted Bergman spaces with exponential weights. First, we give explicit expressions for the upper bounds of Korenblum constants for the weighted Fock spaces. Then, we obtain upper bounds of such constants for the weighted Bergman spaces. Finally, we show a failure of the Korenblum Maximum Principle for weighted Bergman spaces $A^p_\alpha (\mathbb {D})$, where $0<p<1$, $\alpha >0$.

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