报 告 题 目：On the L^p Bergman theory

主 讲 人：张 利 友

单 位：首都师范大学

时 间：6月8日15:00

地 点：公司一楼报告厅

腾 讯 ID：251-419-143

密 码：2484

摘 要：

In the present talk, we’d like to introduce a general L^p Bergman theory on bounded domains in Cⁿ. To indicate the basic difference between L^p and L² cases, we show that the p-Bergman kernel K_p(z) is not real-analytic on some bounded complete Reinhardt domains when p > 4 is an even number. By the Calculus of Variations, we get a fundamental reproducing formula. This together with certain techniques from nonlinear analysis of the p-Laplacian yields a number of results, for instance, the off-diagonal L^p Bergman kernel K_p(z,∙) is Holder  continuous of order 12 for p>1 and of order {2(n+2)} for p=1. We also show that the L^p Bergman metric B_p(z;X) tends to the Carath\'eodory metric C(z;X) as p and the generalized Levi for i∂{ ̅∂log^Kp(z;X) is no less than  B_p(z;X)² for P≥2 and C(z;X)² for P≤2. If time permits, we will also talk about the stability of K_p(z,w) or B_p(z;X) as p varies and the boundary behavior of K_p(z). The talk is based on a joint work with Bo-Yong Chen.

简 介：

张利友，首都师范大学数学科学学院教授，博士生导师。2007年博士毕业于首都师范大学，导师殷慰萍教授。2007-2009年中科院数学所博士后，合作导师陆启铿院士。主持国家自然科学基金面上项目（2项），青年基金（1项），北京市自然科学基金面上项目（1项）。获得首届北京市优秀博士学位论文、中科院王宽诚博士后人才工作奖励。与人合作相关研究成果发表在Adv. Math., JFA, Trans. AMS等国际期刊上。