In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.
The principles of the new maximal operator H * we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz H p , qX[0,1)to the Lorentz LX p , q[0,1) for 1/2 < p <∞ , 0
在这份报纸，为 Banach-space-valued 弱强壮的常规鞅空间 w p H S (X) 的一条原子分解定理被给。作为应用， p-smoothable Banach 空格以在 Banach-space-valued 弱强壮的常规鞅空间 w p H S (X) 上定义的围住的 sublinear 操作员被描绘。
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.
