Moment duality and an improved lower bound for Korenblum's constant

Frank Wikström

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arXiv · 2607.17748

Moment duality and an improved lower bound for Korenblum's constant

Frank Wikström

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Abstract

We introduce a moment-duality method for Korenblum's maximum principle in the Bergman space $A^2(\mathbb{D})$. Starting from an annular coefficient estimate of Wang, we show that admissibility of a constant~$c$ follows from the existence of a probability measure on $[c^2,1]$ whose ordinary and weighted moments lie on opposite sides of the Bergman moments $1/(k+1)$. This converts the norm comparison into a positive moment problem. We then give an explicit measure, consisting of eight atoms with rational data and Lebesgue measure on a terminal interval, for which the required inequalities admit a rigorous ball-arithmetic certificate. Consequently, \[ c_2\geq 0.4263, \] improving Wang's recent lower bound $c_2\geq0.3554$.

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Frank Wikström. 2026-07-20. Moment duality and an improved lower bound for Korenblum's constant. https://arxiv.org/abs/2607.17748

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