广州数学大讲坛第一期

第二讲——纽约州立大学赵如汉教授学术报告

题目：On a class of generalized Berezin type operators on the unit ball of $\mathbb{C}^n$

时间：2025年1月13日（周一）下午3：00——4：00

地点：理学实验楼314

报告人：赵如汉 教授

摘要：We characterize boundedness of a class of generalized Berezin type operators $S_\mu^{s, \beta, r}$ from a weighted Bergman space to a weighted Lebesgue space on the unit ball of $\mathbb{C}^n$. By an improved method using Khinchine's inequality and Khinchine-Kahane-Kalton inequality, our result not only extends a previous result on these operators to a large scale, but also removes an extra restrictive condition to that result. When $(s, \beta, r)=(0, \beta, 1)$, our result also recovers a recent result on boundedness of Berezin type operators. As an application, we provide an alternate proof of a necessary condition for the parameter $c$ in the $L^p_{\alpha}-L^q_{\beta}$ boundedenss of the Forelli-Rudin type operator $S_{a,b,c}$.

报告人简介：

Ruhan Zhao is a SUNY Distinguished Professor in mathematics at the State University of New York Brockport. He obtained PhD in mathematics at University of Joensuu (now University of Eastern Finland) in 1996. In 1998-99, he held a post-doctoral fellowship at Kyoto University, sponsored by the Japanese Society of Promotion of Science (JSPS). He has published over 70 research papers on spaces of analytic functions and operator theory in journals such as Math. Ann., Trans. Amer. Math. Soc., Proc. Amer. Math. Soc., Indiana Univ. Math. J., Michigan Math. J., Pacific J. Math., J. London Math. Soc., etc. In 1995 he introduced the Qp spaces with his coauthors, Rauno Aulaskari and Jie Xiao. In 1996 he introduced F(p,q,s) spaces. The Qp spaces and the F(p,q,s) spaces have been extensively studied by mathematicians all over the world since they were introduced. In 2010 Mathematics Subject Classification (MSC) it assigned Qp spaces a classification number, 30H25. In 2014 Dr. Zhao received the SUNY Chancellor’s Award for Excellence in Scholarship and Creative Activities. Dr. Zhao is also a science fiction writer who published dozens of science fiction stories in China.