广义鞅变换算子的Orlicz范数不等式及其应用

The Orlicz Norm Inequalities for Generalized Martingale Transfrom Operators

证明了由算子值乘子序列所生成的广义鞅变换算子的Orlicz范数不等式,作为应用,给出了证明Banach空间值鞅的极大函数与p阶均方函数的Orlicz范数不等式的一种新方法,其结果刻画了Banach空间的一致光滑性和一致凸性.

The Ф inequalities for the generalized martingale transform operators with operator-valued multiplying sequence are proved. As an application, a new method to prove the Ф inequalities between the maximal functions and the p -mean functions of Banach space-valued martingales is presented. Some geometric properties of the underlying Banach spaces are also considered.