复空间的PL凸性与解析鞅不等式

数学物理学报 ›› 1997, Vol. 17 ›› Issue (1): 64-73.

复空间的PL凸性与解析鞅不等式

Bekjan Turdebek N^1,2

1 武汉大学数学系武汉 430072;
2 新疆大学数学系乌鲁木齐 830046

收稿日期:1995-03-06 修回日期:1995-09-14 出版日期:1997-02-26 发布日期:1997-02-26

Uniformly PL-Convexity of Complex Spaces and Inequalities of Analytic Martingale

Bekjan Turdebek N^1,2

1 Department of Mathematics Wuhan University, Wuhan 430072;
2 Department of Mathematics Xinjiang University Urumqi 830046

Received:1995-03-06 Revised:1995-09-14 Online:1997-02-26 Published:1997-02-26

摘要/Abstract

摘要： 该文研究了取值于复拟Banach空间的解析鞅不等式与该空间的PL一致凸性的关系,证明了解析鞅的q均方函数的弱(1,1)型,强(p,p)型和凸Φ中函数不等式,并应用它们给出了复空间的q一致PL可凸性的等价条件,同时借助解析鞅q均方函数的增长速度给出了同样的刻划.

关键词: 复拟Banach空间, 解析鞅, q-均方函数, 一致PL凸性

Abstract: We study the relationships between some inequalities of ananlytic martingale with values in complex quasi-Banach space and uniformly PL-convexitiable of the space. We prove weak type (1,1), strong type (p, p) and a Φ inequalities of q-mean sequare funiction of analytic martingales with values in quasi-Banach space. Appling them to give some equivalent conditons of q -uniformly PL-convexitiable of the spaces. At the same time, appling growth velocity of q-mean square funicton of analytic martingales give characterization of q-uniformly PL-convexitiable spaces.

Key words: Complex Quasi-Banach space, q-uniformly PL-convex, analytic martingale

Bekjan Turdebek N. 复空间的PL凸性与解析鞅不等式[J]. 数学物理学报, 1997, 17(1): 64-73.

Bekjan Turdebek N. Uniformly PL-Convexity of Complex Spaces and Inequalities of Analytic Martingale[J]. Acta mathematica scientia,Series A, 1997, 17(1): 64-73.