AI 中文总结
本文建立带余项的改进型卡尔森积分不等式，通过类似方法推导卡尔森与朗道的离散不等式，刻画有限和情形下卡尔森不等式的最优常数。
AI 中文摘要
本文建立了卡尔森积分不等式的改进形式，其带有一个涉及与极值函数集相对距离的余项项。采用类似方法可推导卡尔森和朗道的离散不等式，并对有限和情形下卡尔森不等式的最优常数给出另一种刻画。
英文摘要
A sharpened version of Carlson's integral inequality is established, which features a remainder term involving a relative distance to the set of extremal functions. A similar approach leads to an alternative derivation of Carlson's and Landau's discrete inequalities and provides another characterization of the optimal constant in Carlson's inequality for finite sums.
