本项目的课题属于复分析（全纯函数空间、几何函数论）和算子理论，并涉及偏微分方程和位势理论。我们将计算或估计C^n中单位球上Bergman投影和Cauchy变换的p-范数、Siegel上半空间、极小球、四类典型域上的Berezin变换以及R^n中单位球和上半空间上的调和Berezin变换的p-范数；我们将研究R^n中单位球上多调和函数的细胞分解和加权可积性；我们也将考虑共形映射的积分平均谱和Bergman投影的渐近方差估计。

The subjects of this project belong to complex analysis (spaces of holomorphic functions, geometric function theory) and operator theory, which are also related to PDEs and potential theory. We will compute or give estimates of the p-norms of the Bergman projection and the Cauchy transform on the unit ball of C^n, as well as the p-norms of the Berezin transforms on the Siegel upper half-space, the minimal ball and the classical domains in C^n. We also consider the p-norms of the harmonic Berezin transforms on the unit ball and the upper half-space of R^n. Also, we study the cellular decomposition and the weighted integrability of the polyharmonic functions. Besides, we will investigate the integral means spectra of univalent functions and the asymptotic variance of the Bergman projection.