Banach空间值弱Garsia型鞅空间及其原子分解(英文)

Banach Space-Valued Weak Martingale Garsia Spaces and Atomic Decompositions

定义了Banach空间值弱Garsia型鞅空间和三种类型原子,证明了Banach空间值弱Garsia型鞅空间上的四个原子分解定理,并利用这些定理,得到Banach空间值弱Garsia型鞅空间的互相嵌入关系,其结果与Banach空间的凸性和光滑性有密切关系.

Some theorems of atomic decomposition for weak Garsia spaces of Banach space-valued martingales are established, applying them, the embedding relationships among these martingale spaces are discussed,and the results obtained here are connected closely with the geometric properties of the Banach space.