2026/07/20 by Frank Wikström
#math.CV
We introduce a moment-duality method for Korenblum's maximum principle in the Bergman space A2(\mathbbD). 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 [c2,1] 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, c2≥ 0.4263, improving Wang's recent lower bound c2≥0.3554.