1 Notions and LemmasIn this paper,denote by f={F_n,f_n,n≥0),or f=(f_n)_(n≥0) if there is no confu-sion,the bounded martingale in L^2,f_0=0.Let h(x) be a strictly increasing continousfunction,h(0)=0,Φ(x) be a convex...1 Notions and LemmasIn this paper,denote by f={F_n,f_n,n≥0),or f=(f_n)_(n≥0) if there is no confu-sion,the bounded martingale in L^2,f_0=0.Let h(x) be a strictly increasing continousfunction,h(0)=0,Φ(x) be a convex function.Composite function of Φand h(h^(-1),resp) is denoted by Φ(h)(Φ(h^(-1)),resp).Super-exponent(sub-exponent,resp) of Φisdenoted by p_Φ(q_Φ,resp).Here,convex function Φand Φ(h)(Φ(h^(-1)),resp) with condi-tion,unless otherwise stated,in [3].Symbols,notions and properties of convex func-展开更多
基金Supported by the Foundation of Education Ministry,Yunnan Province,China(2013Y578)the Foundation of the Research Item of Strong Department of Engineering Innovation,which is sponsored by Hanshan Normal University,China in 2013
文摘1 Notions and LemmasIn this paper,denote by f={F_n,f_n,n≥0),or f=(f_n)_(n≥0) if there is no confu-sion,the bounded martingale in L^2,f_0=0.Let h(x) be a strictly increasing continousfunction,h(0)=0,Φ(x) be a convex function.Composite function of Φand h(h^(-1),resp) is denoted by Φ(h)(Φ(h^(-1)),resp).Super-exponent(sub-exponent,resp) of Φisdenoted by p_Φ(q_Φ,resp).Here,convex function Φand Φ(h)(Φ(h^(-1)),resp) with condi-tion,unless otherwise stated,in [3].Symbols,notions and properties of convex func-
