乘子算子以及奇异积分算子在局部乘积Hardy空间上的有界性

在本项目中，我们将会研究一些关于多线性多参数傅里叶乘子和非齐次的Journé型奇异积分算子的一些重要的开放的问题。我们的研究主要包含两个方面。一方面我们计划建立具有最佳光滑性的多参数多线性Hörmander型乘子定理且试着建立第一个关于多参数多线性乘子在乘积Hardy空间的有界性。另一方面，我们的项目也包含了非齐次Journé型奇异积分算子的有界性，我们的目标是给出其在有界性的一个充分必要条件。

In this project, we will investigate some important open problems about boundedness of multi-linear and multi-parameter Fourier multipliers and inhomegeneous Journé type singular integral operators. Our research plan mainly include two aspects. On the one hand, we plan to establish Hörmander type theorem for the multi-parameter and multi-linear Fourier multipliers with minimal smoothness and try to firstly prove multi-parameter estimates for them. On the other hand, our project also includes the study of boundedness of inhomegeneous Journé type singular integral operators, we aim to find both the sufficient and necessary conditions to guarantee the corresponding boundedness.