Structures of Banach function spaces that are derived from the theory of martingales

作为这项研究的结果，我们得到了许多定理，这些定理表明我们可以用鞅理论来分析Banach函数空间的某些结构。例如，我们证明了当X是Banach函数空间时，用X的重排不变性和X的Boyd指数来表示X中保证某些鞅不等式有效的充要条件。这一结果表明，鞅不等式的有效性与Banach函数空间的结构之间有着密切的联系。

As a consequence of this research, we obtained a lot of theorems which show that we can analyze some structures of Banach function spaces by using martingale theory. For example we proved that, when X is a Banach function space, somenecessary and sufficient conditions which ensure that certain kinds of martingaleinequalities are valid in X can be expressed in terms of the rearrangement-invariance of X and the Boyd indices of X. This result shows that there are close connections between the validity of martingale inequalities and the structures of Banach function spaces.