题目：L^p Estimates of Singular Integrals and Elliptic Equations 

报告人：李东升 教授（西安交通大学）

Abstract：

This is a series of talks. We will not only go over all the classical results of L^p estimate, but also present some new developments in this field. The detailed proofs will be discussed. We will maintain consistency of the spirit of the proofs that is by accelerating the decay rates of the distribution functions to obtain L^p estimates. The talks are organized as follows.In the first talk, we will mainly discuss L^p estimates for linear elliptic equations. The Calderon-Zygmund estimates will not be used. We use harmonic functions to approach solutions at each scales and then accelerate the decay rates of the distribution functions from L^2 estimates.In the second talk, we will give a new proof of L^p estimates for Calderon-Zygmund type singular integrals. Our new proof contains three steps. In the first step, we show L^2 estimates, which is the same as the original proof of Calderon-Zygmund’s. In the second step, we show L^p estimates for p>2 by accelerating the decay rates of the distribution functions. In the last step, by duality, we obtain L^p estimates for 1<p<2.In the third talk, we will present L^p estimates for fully nonlinear elliptic equations. We will discuss L.Caffarelli’s classical result and then give a generalization of it. 

时间：2020年1月3日（周五）上午9:30-11:30

   2020年1月4日（周六）下午2:30-4:30

   2020年1月5日（周日）下午2:30-4:30

地点：565net必赢客户端本部教二627教室

联系人：酒全森

欢迎全体师生积极参加！