(untitled) (Analysis in Theory and Applications, 2023)
There is a singular integral operators S_φ on the Fock space F^2(C), which originated from the unitarily equivalent version of the Hilbert transform on L^2(R). In this paper, we give an analytic characterization of functions φ with finite zeros such that the integral operator S_φ is bounded on F^2(C) using Hadamard’s factorization theorem. As an application, we obtain a complete characterization for such symbol functions φ such that the Berezin transform of S_φ is bounded while the operator S_φ is not. Also, the corresponding problem in higher dimensions is considered.