报告1：Reversed Hardy-Littlewood-Sobolev inequalities with weights on the Heisenberg group

时间：2023.4.22 18:30-19:20   

腾讯会议：918-607-149

摘要：In this talk, we give some reverse weighted Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. We then show the existence of extremal functions for the above inequalities by combining subcritical approach and renormalization method. Moreover, we obtain the regularity of positive solutions to the Euler-Lagrange equations.

报告 2： Improved Hardy-Littlewood-Sobolev inequality on $S^n $ under constraints

时间：2023.4.22 19:30-20:20   

腾讯会议：918-607-149

摘要：In this talk, we present an improved Hardy-Littlewood-Sobolev inequality under higher-order moments constraint. Moreover, by constructing precise test functions, using improved Hardy-Littlewood-Sobolev inequality, we show such inequality is almost optimal in critical case. As an application, we give a simpler proof of the existence of the maximizer for conformal Hardy-Littlewood-Sobolev inequality.

报告人介绍：

胡云云，陕西师范大学助理研究员。2020年博士毕业于美国叶史瓦大学。主持国家自然科学基金青年项目一项，博士后面上基金一项。主要研究分数阶方程、几何不等式及其极值问题。相关研究结果发表在包括Adv. Math.、 J. Funct. Anal.、Stud. Math、Nonlinear Anal 等学术期刊。