本项目的课题属于多复变函数论和算子理论。我们将研究第二类Siegel域上的函数空间和算子理论。具体地说，我们将计算或估计第二类Siegel域上Bergman投影和Cauchy变换的p-范数，研究Siegel上半空间上Bergman空间上的Toeplitz算子和复合算子，着力于刻画Siegel上半空间上Bergman空间上紧算子和解决Siegel上半空间上的Toeplitz乘积问题（Sarason猜想）。我们还将开展第二类Siegel域上Bloch空间和Besov空间的研究。

The subjects of this project belong to complex analysis (several complex variables) and operator theory. we will investigate the spaces of holomorphic functions and operator theory over homogeneous Siegel domains of type II. In particular, we will compute or give estimates of the p-norms of the Bergman projection and the Cauchy transform on homogeneous Siegel domains of type II, and investigate the Toeplitz operators and the composition operators on the Bergman spaces over the Siegel upper half-space. We will focus on a complete characterization of the compact operators on the Bergman spaces over the Siegel upper half-space (in terms of the Berezin transform) and the attempt to solve Sarason’s Toeplitz product problem (the Sarason conjecture) in the setting of the Siegel upper half-space. We will also investigate the Bloch space and the Besov space on on homogeneous Siegel domains of type II.