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复空间的凸性与Hardy鞅不等式
引用本文:刘培德,Turdebek N.Bekjan.复空间的凸性与Hardy鞅不等式[J].数学学报,1997,40(1):133-143.
作者姓名:刘培德  Turdebek N.Bekjan
作者单位:武汉大学数学系 武汉430072 (刘培德),新疆大学数学系 乌鲁木齐830046(Turdebek N.Bekjan)
摘    要: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.

关 键 词:复拟Banach空间  解析一致凸性  Hardy鞅  Brown运动
收稿时间:1994-12-28
修稿时间:1996-5-13

Inequalities of Hardy Martingales and Convexity in Complex Space
Liu Peide.Inequalities of Hardy Martingales and Convexity in Complex Space[J].Acta Mathematica Sinica,1997,40(1):133-143.
Authors:Liu Peide
Institution:Liu Peide (Department of Mathematics, Wuhan University, Wuhan 430072, China) (Fax: 027-7882661, E-mail: peide @ math, whcnc.ac.cn) Turdebek, N. Bekjan (Department of Mathematics, Xinjiang University, Urumuqi 830046, China)
Abstract: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.
Keywords:Complex quasi-Banach space  Analytic uniform convexity  Hardy martin-gale  Brown motion
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