The Definition And Related Properties Of M_F～p(P>1)

Classic Doob's inequality is one of the most important results in martingale theory and the basis of discussion of the general martingale spaces. But it only estimates the maximum of submartingales for F(x) = xp(p > 1). This paper at first generalize the classic Doob's inequality which can be applied into more general functions. We can again define a series of new spaces of martingales and obtain many resemble properties of general martingale space Mp (p > 1) by deep analysis and discussion. At last, we also define a new space LF(F8) from which many valuable results can be proved by investigation.