首页|Characterizations of Bounded Singular Integral Operators on the Fock Space and Their Berezin Transforms
Characterizations of Bounded Singular Integral Operators on the Fock Space and Their Berezin Transforms
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There is a singular integral operators Sψ 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 ψ with finite zeros such that the integral operatorSψis bounded on F2(C)using Hadamard's factorization theorem.As an application,we obtain a complete characterization for such symbol functions ψ such that the Berezin transform of Sψ is bounded while the operator Sψ is not.Also,the corresponding problem in higher dimensions is considered.
Fock spacesingular integral operatorsboundednessBerezin transform
Xingtang Dong、Li Feng
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School of Mathematics,Tianjin University,Tianjin 300350,China
Natural Science Foundation of Tianjin City of China
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