AI 中文总结
该研究针对伯格曼空间\(A^2(\mathbb{D})\)中的科伦布卢姆极大值原理，引入矩对偶性方法，通过王的环形系数估计，将范数比较转化为正矩问题，给出显式测度并证明，改进了王关于科伦布卢姆常数的下界。
AI 中文摘要
我们为伯格曼空间\(A^2(\mathbb{D})\)中的科伦布卢姆极大值原理引入一种矩对偶性方法。从王的环形系数估计出发，我们表明常数\(c\)的可容许性源于在\([c^2,1]\)上存在一个概率测度，其普通矩和加权矩位于伯格曼矩\(1/(k + 1)\)的两侧。这将范数比较转化为一个正矩问题。然后我们给出一个由八个具有有理数据的原子和一个终端区间上的勒贝格测度组成的显式测度，对于该测度所需不等式有严格的球算术证明。因此，\(c_2\geq0.4263\)，改进了王最近的下界\(c_2\geq0.3554\)。
英文摘要
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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