凹函数定义的弱Orlicz-Hardy空间之间的鞅变换
INTERCHANGE BETWEEN WEAK ORLICE-HARDY SPACES WITH CONCAVE FUNCTIONS THROUGH MARTINGALE TRANSFORMS

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φ1是凹Young函数，φ2是凹或者凸Young函数，且qφ1 > 0，0 < qφ2≤pφ2 <+∞，则当φ1≤φ2时，wHφ1中的元素是wHφ2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 wHφ1 are none other than the martingale transforms of those in wHφ2, where φ1 is a concave Young function, φ2 is a concave or a convex Young function and φ1≤φ2 in 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