BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES |
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引用本文: | Liu Peide(刘培德,Long Ruilin(龙瑞鳞. BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES[J]. 数学年刊B辑(英文版), 1992, 13(2): 167-179 |
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作者姓名: | Liu Peide(刘培德 Long Ruilin(龙瑞鳞 |
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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: | 1990-03-08 |
BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES |
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Affiliation: | 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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