Atomic decompositions of Banach-space-valued martingales. (English) Zbl 0928.46020

Summary: Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such as \(H_\alpha(X)\) and \(_p\widetilde H_\alpha\) in the case \(0<\alpha\leq 1\) are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.


46E40 Spaces of vector- and operator-valued functions
46B20 Geometry and structure of normed linear spaces
60G46 Martingales and classical analysis
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