Harmonic analysis by real variable methods and its applications

我们在欧几里德空间的一个定义域上引入了一个函数空间，并建立了它的基本性质。函数空间在整个欧几里德空间上具有与Fefferman和Stein引入的Hardy空间相似的几个性质。特别地，我们证明了通过具有一定性质的基本定义域的微分同构定义的变量的变换，可以把函数空间变换成另一个相同类型的函数空间。我们利用函数空间研究经典正交级数。我们研究了时频分析领域中使用的其他几个函数空间，并得到了一些关于作用于这些空间中的算子的结果。

We introduced a function space on a domain of the Euclidean space and established its fundamental properties. The function space has several properties similar to the Hardy space on the whole Euclidean space introduced by Fefferman and Stein. In particular, we showed that the change of variables defined through diffeomorphisms, with certain properties, of the basic domains transforms the function space into another function space of the same kind. We used the function space to study classical orthogonal series. We investigated several other function spaces used in the field of time-frequency analysis and obtained several results concerning the operators acting in those spaces.