凹函数定义的弱Orlicz-Hardy空间之间的鞅变换（英文）  

INTERCHANGE BETWEEN WEAK ORLICE-HARDY SPACES WITH CONCAVE FUNCTIONS THROUGH MARTINGALE TRANSFORMS

作　　者：郭红萍 于林[2] 姜琴 GUO Hong-ping YU Lin JIANG Qin(Department of Mathematics and Finance, Hanjiang Normal University, Shiyan 442000, China School of Science, China Three Gorges University, Yichang 443002, China Department of Computer Science, Hanjiang Normal University, Shiyan 442000, China)

机构地区：[1]汉江师范学院数学与财经系,湖北十堰442000 [2]三峡大学理学院,湖北宜昌443002 [3]汉江师范学院计算机科学系,湖北十堰442000

出　　处：《数学杂志》2017年第1期1-10,共10页Journal of Mathematics

基　　金：Supported by the Science and Technology Research Program for the Education Department of Hubei Province of China(Q20156002)

摘　　要：本文研究了两个弱Orlicz-Hardy鞅空间中元素之间相互转换关系的问题.利用鞅变换的方法,证明了:设Φ_1是凹Young函数,Φ_2是凹或者凸Young函数,且q_(Φ_1)>0,0<q_(Φ_2)≤p_(Φ_2)<+∞,则当Φ_1≤Φ_2时,wH_(Φ_1)中的元素是wH_(Φ_2)中元素的鞅变换的结果,所得结果将已有的相关结论由强型空间(赋范空间)推广到弱型空间(赋拟范空间).In this paper, we consider the interchanging relation between two weak OrliczHardy spaces associated concave functions of martingales. By the means of martingale transform,we prove the result that the elements in weak Orlicz-Hardy space wH（Φ1） are none other than the martingale transforms of those in wH（Φ1）, where Φ1 is a concave Young function, Φ2 is a concave or a convex Young function and Φ1≤Φ2in some sense. It extends the corresponding results in the literature from strong-type spaces to the setting of weak-type spaces, from norm inequalities to quasi-norm inequalities as well.

关 键 词：鞅变换 弱Orlicz-Hardy空间 凹函数 

分 类 号：O211.6[理学—概率论与数理统计]