Operator Theory On Two Kinds Of Weighted Fock Spaces

The operator theory on Fock space is a heat problem in Functional Analysis,the problem has important applications in harmonic analysis and other fields.In this paper,we consider the Hankel products and Haplitz products on FockSobolev spaces.We characterize the bounded,compact and Schatten class membership composition operators on Fock-type spaces.Moreover,we study weighted composition operators acting between different Fock-type spaces.In Chapter 1,we mainly review the research background,research development at home,abroad and research results of the operator on the spaces of holomorphic functions.Firstly,we recall the the properties of composition operators and Toeplitz operators on Fock spaces,and then the two kinds of weighted Fock spaces are introduced.Finally,the main contents and results of this paper are introduced.In Chapter 2,we consider the bounded Hankel product on the Fock-Sobolev spaces.Let f and g be functions in the set of all finite linear combinations of kernel functions,we complete characterize when the semi-commutator of Tf,Tg]on the Fock-Sobolev space of complex pliane is zero,and obtain(Tf,Tg]=0 if and only if at least one of f and g is constant,which is different from the result of Fock space.We also study the boundedness and compactness of the mixed product of Hankel and Toeplitz operators the Fock-Sobolev spaces.In chapter 3,we study the boundedness and compactness of(weighted-)composition operators on the Fock-type spaces.We also characterize the Spectra and Schatten class of composition operators on Fock-type spaces.Moreover,we obtain the equivalent conditions for the self-adjointness and unitarity of the weighted composition operator on Fock-type spaces,which are different with those operators on the Fock spaces.