鞅论中一个关于H_(1)■L_(u)^(1)的反例  

A Counterexample on H_(1)■L_(u)^(1) in Martingale Theory

作　　者：田洪丽 龙珑 Tian Hongli;Long Long(School of Mathematics and Statistics,Central South University,Changsha 410083,China)

机构地区：[1]中南大学数学与统计学院,长沙410083

出　　处：《数学理论与应用》2021年第1期91-101,共11页Mathematical Theory and Applications

摘　　要：已知当1 <a <p <∞时,有Hp*=HpS=a Kp=Lp成立.一个自然的问题是H1*, H1S和L1之间的关系是什么? 1970年, Davis证明了H1*=H1S.然而,到目前为止很少有关于H1和Lu1之间关系的研究.在本文中,我们通过构造反例的方式说明H1■Lu1,最终得到H1■Lu1■L1.As we have already known that when 1 < a < p < ∞, Hp^(*)= HpS=a Kp = Lp. A natural question is that what the relations among H_(1)^(*), H_(1)S and L^(1)? In 1970, Davis proved that H_(1)^(*)= H_(1)S. However, there are few researches on the relationship between H_(1) and L_(u)^(1) until now. In this paper, we prove that H_(1)■L_(u)^(1) by constructing a counterexample and hence get H_(1)■ L_(u)^(1)■L^(1).

关 键 词：鞅空间 Levi鞅 HARDY空间 

分 类 号：O178[理学—数学]