非倍测度空间上的思想方法的运用在解决著名的Painlevé 问题和 Vitushkin 猜想中起着关键作用，因此，该空间上的奇异积分算子研究有重要的理论意义。.本课题将在前期研究工作的基础上，（一）深入讨论强Calderon-Zygmund算子（非卷积型）在非倍测度Lebesgue空间、Hardy空间中的性质；结合Sharp极大估计以及RBMO函数特征，研究各种强奇异积分算子与RBMO生成的交换子；研究参数型Marcinkiewicz算子、强奇异型Marcinkiewicz算子在非倍测度空间有界性；研究多线性强奇异积分算子、广义强奇异积分算子和超强奇异积分算子在非倍测度函数空间中的相关性质。（二）对诸多学者关注的乘积奇异积分算子，我们也将讨论其在非倍测度空间中的性质问题。本课题将较为系统地研究强奇异积分算子在非倍测度空间上的性质，进一步探索研究该空间的算子性质。

The analysis on the non-doubling measure spaces made an important sense in solving the famous Painleve problem and the Vitushkin conjecture. Therefore, the research of the singular integral operators on this type spaces has important theoretical significance. .In this project, we will discuss the strong Calderon-Zygmund operator (the convolution) in the non-doubling measure Lebesgue space and Hardy space. Based on Sharp type estimates and characteristics RBMO functions, we study the commutators generated by strong singular integral operators and RBMO functions. We will research on the boundedness of parameter Marcinkiewicz operators and strong type Marcinkiewicz operators. And also, we want to obtain some estimates for multilinear strong singular integral operators、generalized strong singular integral operators and super strong singular integral operators under non-doubling measures. On the other hand, we will discuss the product singular integral operators which attracted many research works and are still active nowadays. We will systematically study the strong singular integral operators on the non-doubling measure spaces and provide theoretical support for the further refinement of the operator theory.