学术报告（韩永生 2024.5.13）

摘要： It was well known that geometric considerations enter in a decisive way in many questions of analysis. As Meyer, the recipient of the 2017 Abel Prize, remarked “One is amazed by the dramatic changes that occurred in analysis during the twentieth century. In the 1930s complex methods and Fourier series played a seminal role. After many improvements, mostly achieved by the Calder´on–Zygmund school, the action takes place today on spaces of homogeneous type. No group structure is available, the Fourier transform is missing, but a version of harmonic analysis is still present. Indeed the geometry is conducting the analysis.”

In this talk, we will concentrate on questions that how the geometrical considerations play a crucial role in the theory of singular integrals. We will attempt to give a broad overview of the descriptions of the singular integrals, such as, nonstandard singular integrals which include the flag singular integrals, singular integrals in the Dunkl setting and the singular integrals associated with the Zygmund dilations.