Clarkson不等式与 Banach空间几何(英文)

ON CLARKSON INEQUALITIES AND GEOMETRY OF BANACH SPACES

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 .

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.