论文标题
Khintchine不平等现象的不平等和Banach-Mazur距离的应用
Khintchine inequality on normed spaces and the application to Banach-Mazur distance
论文作者
论文摘要
我们在汉纳类型和cotype的规范空间上建立了变异的khintchine不平等，其中与经典的khintchine不平等相对应的rademacher分布被一般对称分布所取代。证明涉及$ p $ - barycenter和Birkhoff的Ergodic定理。更重要的是，通过采用这些Khintchine不平等，我们在$ l^p $ - 鲍尔和一个中央对称的凸体之间获得了Banach-Mazur距离的一些下限。
We establish variant Khintchine inequalities on normed spaces of Hanner type and cotype, in which the Rademacher distribution corresponding to classical Khintchine inequality is replaced by general symmetric distributions. The proof involves the $p$-barycenter and Birkhoff's ergodic theorem. More importantly, by employing these Khintchine inequalities, we get some lower bounds for Banach-Mazur distance between $l^p$-ball and a general centrally symmetric convex body.
