In this talk, we will introduce several integral estimates. As some applications of these integral estimates, we generalize Forelli-Rudin type operator $S_{\lambda,\tau,c}$ to a kind of logarithmic Forelli-Rudin type operator $Q_{\lambda,\tau,c,k,k'}$, and characterize the boundedness of $Q_{\lambda,\tau,c,k,k'}$ from $L^{p}(B_{n}, dv_{t})$ to $L^{q}(B_{n}, dv_{t})$ for $1\leq p, q\leq+\infty$, where $\lambda, \tau, c, k, k', t$ are real numbers. These results generalize some previous results on Forelli-Rudin type operators by Kures and Zhu in 2006 and Zhao et al in 2015 and 2022.
张学军，湖南师范大学教授，基础数学博士生导师，主要从事多复变函数空间理论和算子理论的研究，到目前为止主持国家级项目两项、湖南省自然科学基金项目三项、湖南省教育厅重点项目两项，在《Sci Sin Math》、《Potential Analysis》、《J Math Anal Appl》、《中国科学》等期刊上发表学术论文120余篇。
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