摘要
Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. Theauthors prove the equivalence of the following two conditions:(i) E1(Mf) < cE2(Zo+A) for every nonnegative submartingale f = (fn)n>o with it'sDoob's Decomposition: f= Z + A, where Z is a martingale in L1 and A is a nonnegativeincrasing and predictable process.(ii) There exists positive constants c, to such that > to.When 1 =2 the condition (ii) above is equivalent to the classical condition p < 1. Asa consequence, for a concave function ,if and only if E1(Mf) < cE2(Zo+A)for every nonnegative submartingale f.
Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. Theauthors prove the equivalence of the following two conditions:(i) E1(Mf) < cE2(Zo+A) for every nonnegative submartingale f = (fn)n>o with it'sDoob's Decomposition: f= Z + A, where Z is a martingale in L1 and A is a nonnegativeincrasing and predictable process.(ii) There exists positive constants c, to such that > to.When 1 =2 the condition (ii) above is equivalent to the classical condition p < 1. Asa consequence, for a concave function ,if and only if E1(Mf) < cE2(Zo+A)for every nonnegative submartingale f.
基金
the National Science Foundation of P.R.China
