| BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES |
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| 作者姓名： | Liu Peide |
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| 作者单位： | Department of Mathematics Wuhan Univeraity Wuhan Hubei 430072 China，Institute of Mathematics Academa Hmica Beijing 100080 China |
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| 摘 要： | The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, the Φ-function nequalitities of sharp operators f_p~#, f_p~#, p-variation operators W_p, W_p and the martingale tranform operator T_v are discussed. It is proved that the boundedness of these operators characterizes the smoothness, convexity and UMD-property of Banach spaces.
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| 收稿时间： | 3/8/1990 12:00:00 AM |
BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES |
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| Institution: | Department of Mathematics,Wuhan University,Wuhan,Hubei 430072,China. and Department of Mathematics,Wuhan University,Wuhan,Hubei 430072,China. |
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| Abstract: | The aim of this paper is establiching some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces.In particular,the $\phi-function$ inequalitities of sharp operators $\widetilde{f_{p}^{\sharp}}$,p-variation operators $W_p$,$\widetilde{W_p}$ and the martingale tranform operator $T_v$ are discussed.It is proved that the boundedness of these operators characterizes the smoothness,convexity and UMD-property of Banach spaces. |
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