首页|DOUBLE Φ-INEQUALITIES FOR BANACH-SPACE-VALUED MARTINGALES
DOUBLE Φ-INEQUALITIES FOR BANACH-SPACE-VALUED MARTINGALES
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NETL
NSTL
维普
万方数据
Let B be a Banach space,Φ1,Φ2 be two generalized convex Φ-functions and Ψ1,Ψ2 the Young complementary functions of Φl,Φ2 respectively with ∫tt0 ψ2(s)/sds≤c0ψ1(c0t) (t＞t0)for some constants c0 ＞ 0 and t0 ＞ 0,where ψ1 and ψ2 are the left-continuous derivative functions of Ψ 1 and Ψ2,respectively.We claim that:(i) If B is isomorphic to a p-uniformly smooth space (or q-uniformly convex space,respectively),then there exists a constant c ＞ 0 such that for any B-valued martingale f =(fn)n≥0,‖f*‖Φ1 ≤ c‖S(p)(f)‖Φ2 (or ‖S(q) (f)‖Φ1 ≤ c‖f* ‖Φ2,respectively),where f* and S(p)(f) are the maximal function and the p-variation function of f respectively; (ii) If B is a UMD space,Tvf is the martingale transform of f with respect to v =(vn)n≥0 (v* ≤ 1),then ‖(Tvf)*‖Φl ≤ c‖f*‖Φ2.
martingaleconvex Φ-inequalitymartingale transformweighted average
Wang Yingzhan、Zhang Chao、Hou Youliang
展开 >
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
This research was supported by the National Natural Science Foundation of China
NETL
NSTL
维普
万方数据
