变差算子及二阶椭圆算子的相关问题

本项目主要探讨调和分析与遍历论以及偏微分方程领域的若干交叉问题。特别地，我们将研究非卷积型奇异积分算子以及粗糙核奇异积分交换子等的变差算子的有界性问题；研究与二阶散度型椭圆算子相关的Kato平方根算子、分数阶微分算子生成的交换子的加权模不等式等相关问题。本项目的研究不仅将丰富和发展现代调和分析理论，而且必将对遍历论和偏微分方程等领域的研究和发展产生新的促进作用。

This project mainly discusses some cross-cutting issues in the fields of harmonic analysis, ergodic theory and partial differential equations. In particular, this project will study the variational inequalities for the non-convolution singular integrals and the commutators of singular integrals with rough kernels; the weighted norm inequalities for the commutators of the Kato square root and the commutators of fractional differential operators associated with the second order divergence form elliptic operators. The study of this project will not only develop and enrich the theory of modern harmonic analysis, but also give a new promotion in the fields of ergodic theory and partial differential equations.