DOUBLE Φ-FUNCTION INEQUALITY FOR NONNEGATIVE SUBMARTINGALES

摘要

The authors establish a kind of inequalities for nonnegative submartingales which depend on two functions　ψ and ψ, and obtain the equivalent conditions for　Φ and ψ such that this kind of inequalities holds. In the caseΦ=ψ ε△2, it is proved that this necessary and sufficient condition is equivalent to qΦ >1.