THE DYADIC DERIVATIVE AND CESRO MEAN OF BANACH-VALUED MARTINGALES  

作　　者：陈丽红 刘培德 

机构地区：[1]School of Mathematics and Statistics,Wuhan University [2]College of Science,Wuhan University of Science and Engineering

出　　处：《Acta Mathematica Scientia》2009年第2期265-275,共11页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (10371093)

摘　　要：In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic to a p-uniformly smooth space （1 〈p ≤ 2）. And it is also bounded from Hra（X） to Lra（X） （0 〈 r 〈 ∞,0 〈 a≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic to a p-uniformly smooth space （1 〈p ≤ 2）. And it is also bounded from Hra（X） to Lra（X） （0 〈 r 〈 ∞,0 〈 a≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.

关 键 词：Hardy-Lorentz space dyadic derivative B-valued martingale Cesaro mean 

分 类 号：O177[理学—数学]