Two papers, “Schatten class Hankel operators on the Segal-Bargmann space and the Berger-Coburn phenomenon” and “Proper mappings between indefinite hyperbolic spaces and Type I classical domains” are recently published in Transactions of the American Mathematical Society. The former is written by Prof. Hu Zhangjian from the Research Team of Several Complex Variables of our university and Professor Jani A. Virtanen from University of Reading. The latter is collaborated by Prof. Tang Xiaomin of our university, Prof. Huang Xiaojun of Rutgers University, Associate Prof. Lu Jin of Anhui University and Prof. Xiao Ming of the University of California, San Diego. This is the first time that scholars of our university have published research results in this world-renowned journal.

The Several Complex Variables Research Team of Huzhou University has been committed to the theoretical research of basic mathematics for a long time, focusing on hot issues and important problems in the holomorphic mapping of multi-complex variables and function space theory, and obtaining high-quality original results. On the high-dimensional complex space, Prof. Hu Zhangjian et al. give a complete characterization of the Hankel operator belonging to the Schatten-p class on the weighted Segal-Bargmann space. The necessary and sufficient conditions that Hankel operator belongs to Schatten-p class are obtained for the intrinsically bounded function on the complex space of high dimension. Prof. Tang Xiaomin et al. studied the rigidity of inverse compactly holomorphic mappings between indefinite hyperbolic Spaces, and generalized the results of Baouendi-Ebenfelt-Huang and Ng. At the same time, descriptions are given about the rigidity of the inverse compact holomorphic mapping on the first class of typical fields, solving a conjecture given by Chan. These research work are supported by the National Natural Science Foundation of China and the Natural Science Foundation of Zhejiang Province.

Transactions of the American Mathematical Society, Founded in 1900, is a comprehensive mathematical journal sponsored by the American Mathematical Society, with more than 200 papers annually. The journal is committed to publishing breakthrough results in all branches of pure mathematics and applied mathematics, and is recognized as the top journal of mathematics in the industry, with a high academic reputation.

Thesis links：

[1] https://www.ams.org/journals/tran/2022-375-05/S0002-9947-2022-08638-4/?active=current

[2] https://www.ams.org/journals/tran/2022-375-12/S0002-9947-2022-08618-9/?active=current