非齐型测度空间上多参数奇异积分算子研究

本项目主要关注非齐型度量测度上的多参数奇异积分算子和函数空间及其在偏微分方程中的应用。我们将致力于解决如下问题：（1).研究乘积Calderon-Zygmund算子和极大算子在非齐型度量测度空间上的Lp有界性，进一步建立相应的T1定理；2) 在非齐型度量测度空间上研究与Stein发展的Flag型奇异积分算子的性质；3）讨论非齐型测度上函数空间的特征刻画；进一步探讨Edge Sobolev 空间上的不等式估计及其在某些区域上的微分方程边值问题中的应用。

This research project is mainly devoted to consider the multi-parameter singular integral operators and function spaces under non-homogeneous metrics measures and their applications in partial differential equation. In this project, we mainly focus on the following problems: 1) The Lp- boundedness of the product Calderon-Zygmund operator，the maximal operator and the T1 theorem on non-homogeneous space with metric measures; 2) Properties of Flag-type singular integral operators developed by Stein in the non-homogeneous type space associated with metric measures; 3) The characterization of the function spaces on non- homogeneous function spaces; study the inequalities in some Edge Sobolev spaces and its application on boundary value problems for differential equations on certain domains.