拟鞅不等式与Banach空间几何性质

拟鞅不等式与Banach空间几何性质 INEQUALITIES FOR QUASI-MARTINGALES AND GEOMETRICAL PROPERTIES OF BANACH SPACES 梁汉营 Liang Hanying 1 2 3 first-author 甘师信 Gan Shixin 1 2 3 武汉大学数学系 武汉大学数学系 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 武汉大学数学系,武汉 武汉大学数学系,武汉 ,430072 ,430072 建立了B值p-拟鞅与其P方函数的包括凸Φ-不等式在内的若干不等式,反过来用这些不等式刻划了Banach空间的凸性和光滑性;并建立了B值拟鞅变换的凸Φ-不等式,得到了UMD空间的刻划,推广和深化了已知鞅的相应结论。 In this paper, some inequalities are established between a p-quasi-martingale and its p-power function. Conversely, convexity and smoothness of Banach spaces are characterized in terms of these inequalities. In other direction, convex Φ inequalities of B valued quasi-martingale transforms are obtained and UMD spaces are characterized as well. Some known results are extended and improved. 拟鞅 拟鞅变换 凸φ-不等式 quasi-martingale quasi-rnartingale transform convex Φ-inequality O177 国家自然科学基金(61672102);高等学校博士学科点基金 1996-01-01 2021-04-01 1