| 复空间的凸性与Hardy鞅不等式 |
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| 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. DOI: cnki:ISSN:0583-1431.0.1997-01-016 |
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| 作者姓名： | 刘培德 Turdebek N.Bekjan |
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| 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) |
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| 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.
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| 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： | 1996-05-13 |
Inequalities of Hardy Martingales and Convexity in Complex Space |
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| Liu Peide. Inequalities of Hardy Martingales and Convexity in Complex Space[J]. Acta Mathematica Sinica, 1997, 40(1): 133-143. DOI: cnki:ISSN:0583-1431.0.1997-01-016 |
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| Authors: | Liu Peide |
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| Affiliation: | 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) |
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| 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. |
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| Keywords: | Complex quasi-Banach space Analytic uniform convexity Hardy martin-gale Brown motion |
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