Atomic decompositions of Banach-spacevalued martingales
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Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such asH α(X) andρ H α in the case 0< α⩽ are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.
KeywordsBanach-space-valued martingale martingale space atomic decomposition geometry of Banach space
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