BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES

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.