本项目以Berezin变换为研究对象, 重点研究推广的Berezin变换及Berezin-型变换在L^p空间上的有界性及精确范数. 进一步, 在实单位球的情形下, 运用Berezin变换的性质, 探讨调和函数空间上的Toeplitz算子代数的紧性刻画. 结合超几何函数与Möbius变换的性质, 本项目采用新的方法探索函数空间与算子理论的热点问题.

This project is on the research of the Berezin transform. And it is mainly on the boundedness and the exact norm of extended Berezin transform and Berezin-type transform on L^p spaces. Moreover, using the properties of the Berezin transform, we discuss the compactness of Toeplitz operators algebras on harmonic function spaces on the real unit ball. Combined the properties of the hypergeometric function and Möbius transform, the project uses new methods to explore the hot topics on function spaces and operators theory.