主 题: Geometry and Analysis
报告人: Prof. Han Yongsheng ( Auburn University, USA )
时 间: 2014-06-04 16:00-17:00
地 点: 理科一号楼1418（主持人：刘和平）
Geometric considerations enter in a decisive way in many questions of harmonic analysis. In explicit form such ideas arose first in the estimation of the Fourier transform of surface-carried measure; they have since played a key role in averages over lower-dimensional varieties, restriction theorems, in connection with the study of oscillatory integrals and Fourier integral operators, and in application to linear and non-linear dispersive equations.
In this talk, we will consider another fundamental occurrence of geometric concepts related to singular integrals and function spaces. The classical theory of Calderon-Zygmund singular integral operators as well as the theory of function spaces were based on extensive use of convolution operators and on the Fourier transform. However, it is now possible to extend most of those ideas and results to spaces of homogeneous type. As Meyer remarked in his preface to the book written by Deng Donggao and Han Yongsheng, “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 Calderon-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 describe how the geometry conducts the analysis on spaces of homogeneous type introduced by Coifman and Weiss in the early 1970s.
