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| BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES |
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Citation： |
Liu Peide(刘培德）,Long Ruilin（龙瑞鳞）.BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES[J].Chinese Annals of Mathematics B,1992,13(2):167~179 |
| Page view： 849
Net amount： 666 |
Authors： |
Liu Peide(刘培德）; Long Ruilin（龙瑞鳞） |
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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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