次正规条件下0<p≤1时的鞅Hardy空间

Martingale Hardy spaces with 0<p≤1 under the subregularity condition

在一般情况下 ,p >1时的鞅不等式及鞅变换不等式在 0 <p≤ 1时不成立 ,在正规条件下这些不等式才能成立 ,但正规条件要求过高 ,引进了次正规条件 ,在这一条件下 ,对于 0 <p≤ 1的鞅Hardy空间H p 、HSp、Hsp 是等价的 ;

It is well known that many of the inequalities of martingales and martingale transforms which hold for p>1?do not hold for ?0<p≤1, but they are true under the regularity condition. In this paper, the so-called subregularity condition is introduced under which the equivalence relations of martingale Hardy spaces H * p,H S p and H s p and some inequalities of martingale transforms are proved for 0<p≤1.