向量值弱Hardy鞅空间的弱原子鞅分解

On Weak Atomic Martingale Decompositions of Vector-Valued Weak Hardy Spaces of Martingales

引入了弱原子鞅与正则弱原子鞅的概念,研究了两类Banach空间值弱Hardy鞅空间的弱原子鞅分解和正则弱原子鞅分解,所得结论揭示了弱Hardy鞅空间正则弱原子鞅分解的存在性与Banach空间一致光滑性和一致凸性之间的内在联系.

The concepts of weak atomic martingales and regular weak atomic martingales are introduced before the weak atomic decompositions of martingale in two classes of Banach-space-valued martingale Hardy spaces are investigated in this paper.The results show that the internal relations between the existence of regular weak atomic decompositions of martingale and the uniform smoothness and uniform convexity of Banach spaces are exposed.