复空间的凸性与Hardy鞅不等式

Inequalities of Hardy Martingales and Convexity in Complex Space

本文研究了取值于复拟Banach空间的一种特殊类型的鞅——Hardy鞅的不等式与该空间的解析一致凸性的关系,证明了Hardy鞅的q均方函数的弱(1,1)型,强(p,p)型和凸φ函数的不等式,并应用它们给出了复空间的解析q一致可凸性的等价条件.同时借助于复平面单位圆中的Banach空间值解析函数和Brown运动给出了同样的刻划.

In this paper we study the relationships of inequalities of Hardy martingales with values in complex quasi-Banach space and analytic uniform convexity of the space, prove weak (1,1), strong (p,p) and convex φ-function inequalities of q-mean-square function of Hardy martingales, and using them give characterizations of analytic q-uniform convexifiablity of complex space. In the same time we characterize the same property by using Banach-space-valued analytic functions and Brown motion in unit disk of complex plane.