论文标题
加权的prékopa-leindler不平等和与准蛋白酶的总和
A Weighted Prékopa-Leindler inequality and sumsets with quasicubes
论文作者
论文摘要
我们给出了四个作者论文的两个关键结果的简短，独立的证明。第一个是一种加权的离散prékopa-leindler不平等。然后将其应用于表明，如果$ a，b \ subseteq \ mathbb {z}^d $是有限集，而$ u $是“ quasicube”的子集，则是$ | a + b + u | \ geq | a |^{1/2} | b |^{1/2} | u | $。该结果是第五作者和Pälvölgyi在汇总现象中即将进行的工作中的关键要素。
We give a short, self-contained proof of two key results from a paper of four of the authors. The first is a kind of weighted discrete Prékopa-Leindler inequality. This is then applied to show that if $A, B \subseteq \mathbb{Z}^d$ are finite sets and $U$ is a subset of a "quasicube" then $|A + B + U| \geq |A|^{1/2} |B|^{1/2} |U|$. This result is a key ingredient in forthcoming work of the fifth author and Pälvölgyi on the sum-product phenomenon.
