鞅p-均方函数的B-G-D双Φ-不等式

Inequalities of Two Φ-functions of B-G-D to p-variations for Martingales

设定义在[0,∞)上Φ1,Φ2是凸函数,对于鞅的p-均方算子和极大算子,当Φ1,Φ2满足一定条件时,证明Burkholder-Gundy-Davis不等式关于Φ1,Φ2的Orlicz范数不等式,并通过构造具体的鞅说明这个条件是充分的.

Let Φ1,Φ2 be convex functions. For p - variation operator and Maximal operator of martingales, the （Φ1,Φ2）-inequalities of Orlicz norm on Burkholder-Gundy-Davis are proved in the certain condition. It is explained that the condition is sufficient by constructing a martingale.