| Clarkson不等式与Banach空间几何 |
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| 引用本文： | 黄海军.Clarkson不等式与Banach空间几何[J].数学杂志,2001,21(2):173-177. |
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| 作者姓名： | 黄海军 |
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| 作者单位： | 武汉大学数学系 |
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| 基金项目： | Supported by the National Natural Science Foundation of China and "Zhiqiang” Foundation of Whuan University. |
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| 摘 要： | 我们证明了Banach空间X是Clarkson p型（q余型）当且仅当X是一个特殊的p一致光滑空间（q-一致凸空间（）,我们还找到刻划型（余型）的一系列鞅不等式,同时,我们得到了均方函数sharp不等式。
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| 关 键 词： | Walsh－Paley鞅 一致凸 一致光滑 Clarkson不等式 Banach空间 鞅不等式 |
| 文章编号： | 0255-7797(2001)02-0173-05 |
ON CLARKSON INEQUALITIES AND GEOMETRY OF BANACH SPACES |
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| HUANG Hai-jun.ON CLARKSON INEQUALITIES AND GEOMETRY OF BANACH SPACES[J].Journal of Mathematics,2001,21(2):173-177. |
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| Authors: | HUANG Hai-jun |
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| Abstract: | It is shown that a Banach space X is of Clarkson type p(cotype q) if and only if X is a special uniformly smooth space(or q uniformly convex space). We also find a series of martingale inequalities to characatize Clarkson type p(cotype q) spaces. At the same time, we get the sharp inequalities of mean-square-function of martingales. |
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| Keywords: | Walsh-Paley martingale uniform convexity uniform smoothness Clarkson's inequality |
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