Operator-valued martingale transforms in rearrangement invariant spaces and applications

查看全文 作　　者：JIAO [1]Yong;WU [1]Lian;POPA [2]Mihai

机构地区：[1]Institute of Probability and Statistics,Central South University;[2]Department of Mathematics and Statistics,Queen's University

出　　处：《Science China Mathematics》索引2013年第56卷第4期,共14页

基　　金：supported by National Natural Science Foundation of China (GrantNo. 11001273);Research Fund for International Young Scientists (Grant No. 11150110456);Research Fundfor the Doctoral Program of Higher Education of China (Grant No. 20100162120035);Postdoctoral Science Foundation of China and Central South University 摘　　要：In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved.Some well-known results are generalized and unified.Applications are given to classical operators such as the maximal operator and the p-variation operator of vector-valued martingales,then we can very easily obtain some new vector-valued martingale inequalities in rearrangement invariant function spaces.These inequalities are closely related to both the geometrical properties of the underlying Banach spaces and the Boyd indices of the rearrangement invariant function spaces.Finally we give an equivalent characterization of UMD Banach lattices,and also prove the Fefferman-Stein theorem in the rearrangement invariant function spaces setting. 关键词：功能空间鞅变换重排应用算子函数空间 BANACH 鞅不等式

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Operator-valued martingale transforms in rearrangement invariant spaces and applications

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