报告题目：On the compactness of Bergman-type integral operators

报告人：丁立家 北京大学

报告时间：2021年4月23日 10:00-11:00

报告地点：腾讯会议885253029

报告摘要：In this talk, we will mainly discuss the compactness of two kinds of Bergman-type integral operators $K_\alpha,K_\alpha^+$ on the complex unit ball, which are all kernel integral operators induced by the Bergman kernel on the unit ball. We first give the characterization of the $L^p$-$L^q$ compactness of operators $K_\alpha,K_\alpha^+$; indeed, we will see that the $L^p$-$L^q$ compactness of operators $K_\alpha,K_\alpha^+$ is equivalent. Moreover, we will completely characterize Schatten class and Macaev class Bergman-type integral operators $K_\alpha$ on the $L^2$-space and the Bergman space via inequalities related to the dimension of the unit ball; we also give a relatively intrinsic characterization by introducing a concept of dimension of a compact operator.

报告人简介：丁立家，北京大学数学科学学院博士后, 主要从事算子理论领域的研究，特别是单位球和有界对称域上的算子理论，已取得若干重要成果。