报告专家：宋亮教授（中山大学）

报告题目：Characterizations of CMO spaces associated to Schrodinger operators and their application

报告地点：腾讯会议 ID: 972632272

报告时间:  2022年4月12日上午8:20

报告简介：Let L be a Schr\"odinger operator of the form L=-\Delta+V acting on L^2(\mathbbR^n) where the nonnegative potential V belongs to the reverse H\"older class RH_q for some q\geq (n+1)/2. Let CMO_L(\mathbb{R}^n) denote the function space of vanishing mean oscillation associated to L. In this talk, we will show that a function f of CMO_L(\mathbb{R}^n) is the trace of the solution to \mathbb{L}u= -u_{tt} +Lu=0, u(x,0)=f(x), if and only if, u satisfies a kind of Vanishing Carleson condition. This continues the lines of the previous characterizations by Duong, Yan and Zhang, and Jiang and Li for the BMO_L spaces, which were founded by Fabes, Johnson and Neri for the classical BMO space. For this purpose, we will prove two new characterizations of the CMO_L(\mathbb{R}^n) space, in terms of mean oscillation and the theory of tent spaces, respectively.

报告人简介：中山大学教授。2001年获中山大学学士学位，2006年获中山大学博士学位，同年留校任教。2017年获聘中山大学数学学院教授。主要从事调和分析函数空间理论及均匀化理论方面的理论等方面研究。他与合作者得到了：(1)与一般的微分算子相联系的Hardy空间的极大函数刻画；(2)发展了与微分算子相联系的VMO空间及其对偶理论；(3)证明了非光滑区域上Maxwell型椭圆方程的一致Lp估计。已在Adv. Math.，ARMA， J. Funct. Anal.等国际著名数学期刊上发表多篇论文，引起国内外同行的关注。2016年入选国家优青项目基金。