凹函数定义的Orlicz-Hardy鞅空间上的鞅变换

Martingale Transform on Orlicz-Hardy Spaces Associated with Concave Functions

以鞅变换为工具,刻画了Orlicz-Hardy鞅空间之间的相互关系.即采用构造性方法,证明了如下结论:(1)设Φ_1是凹函数,其下指标q_(Φ_1)>0,Φ_2是凸函数,其上指标p_(Φ_2)<∞.则鞅f∈H_(Φ_1)~s,当且仅当f是H_(Φ_2)~s中某个鞅g的鞅变换;(2)设Φ是凹函数,其下指标q_Φ>0.则鞅f∈H_Φ~s,当且仅当f是BMO_2中某个鞅g的鞅变换.

Making use of the technique of Burkholder＇s martingale transforms,the ＂characterization＂ about interchanging between Orlicz-Hardy spaces associated with concave functions of martingales is investigated.Accurately speaking,the following results are proved constructively：（1） Let Φ_1 be a concave Young function with qΦ_1 0and Φ_2 be a convex Young function with pΦ_2∞,then the elements in Orlicz-Hardy space H^s_Φ_1 are none other than the martingale transforms of those in H^s_Φ_2;（2） Let Φbe a concave Young function with qΦ 0,then a martingale f∈H^s_Φ if and only if f is the martingale transform of some martingale g ∈ BMO_2.