弱Orlicz-Hardy空间之间的鞅变换

Martingale Transforms between Weak Orlicz-Hardy Spaces

摘要: 利用Burkholder的鞅变换为工具，刻画了弱Orlicz-Hardy鞅空间之间的相互关系，构造性地证明了：对于任意的两个Young函数 ，且 (某种意义下)，则弱Orlicz-Hardy空间 中的鞅是 中元素的鞅变换；反过来，弱Orlicz-Hardy鞅空间 中的鞅也是 中元素的鞅变换。

Abstract: Using the technique of Burkholder’s martingale transforms, we investigate the correlations between two weak Orlicz-Hardy spaces of martingales. Let and in be two Young functions and in some sense, a constructive proof is obtained of that the elements in weak Orlicz-Hardy space are none other than the martingale transforms of those in weak Orlicz-Hardy space , and vice versa.