Boundedness of Singular integral operators and applications to Bochner-Riesz summability, Riesz transforms, and Hardy spaces.

我们的目标是发展调和分析方法来研究奇异积分算子以及与这些算子相关的函数空间。我们建议研究傅立叶分析中Bochner-Riesz平均的长期收敛问题，并研究作用于粗糙区域上或作用于一般空间类流形上的具有非光滑系数的微分算子。预期结果是调和分析中有待开发的新技术，应用于解决调和分析、偏微分方程和函数空间理论中的一些公开问题。

We aim to develop harmonic analysis methods to study singular integral operators and function spaces associated to these operators. We propose to study the long standing problem of convergence of Bochner-Riesz means in Fourier analysis, and investigate differential operators with non-smooth coefficients acting on rough domains, or acting on general spaces like manifolds. Expected outcomes are new techniques in harmonic analysis to be developed, with applications being solutions to a number of open problems in the theories of harmonic analysis, partial differential equations and function spaces.