摘要
There is a singular integral operators Sj on the Fock space F2(C),which originated from the unitarily equivalent version of the Hilbert transform on L2(R).In this paper,we give an analytic characterization of functions j with finite zeros such that the integral operator Sj is bounded on F2(C)using Hadamard’s factorization theorem.As an application,we obtain a complete characterization for such symbol functions j such that the Berezin transform of Sj is bounded while the operator Sj is not.Also,the corresponding problem in higher dimensions is considered.
基金
supported in part by the Natural Science Foundation of Tianjin City of China(Grant No.19JCQNJC14700).
