Some Kinds Of Integration Operators On Function Spaces Of General Domain

The main research objects of this paper are the weakly localized operators on large Fock spaces,the Toeplitz operators induced by a positive Borel measure on A2 weight harmonic Bergman spaces and integration operators on regular weighted Dirichlet spaces of annulus.In Chapter 1,we mainly introduce the research background and research development at home and abroad.At the same time,the main research results of this paper are also introduced.In Chapter 2,the Toeplitz operators induced by bounded symbols on large Fock spaces are generalized,and a class of generalized operators are obtained,which are called weakly localized operators.Firstly,we prove the boundedness of projection on large Fock spaces Fφp,and the dual spaces of Fφp are obtained when 0<p<00.Also,we conclude the algebraic properties and boundedness of weakly localized operators.Finally,we consider necessary and sufficient conditions for the compactness of weakly localized operators on large Fock spaces.In Chapter 3,Toeplitz operators Tμ:hω2→hω2 induced by a positive Borel measure on A2 weight Bergman spaces are studied.We mainly study necessary and sufficient conditions for bounded and compact Toeplitz operator Tμ.Furthermore,we offer a characterization of the membership in Schatten class of Toeplitz operators Tμ on hω2,where 1 ≤p<∞.In Chapters 4 and 5,we mainly study the boundedness and compactness of a class of integration operators on regular weighted Dirichlet spaces.We show first that the boundedness of projection Pω on Dωp with 0<p<∞.Next,the boundedness of projection Pω1,2 on Dω1,2 p(M)(1<p<∞)is obtained as well.Finally,we get necessary and sufficient conditions for the boundedness and compactness of integration operators Tμ:Dω1,2 p(M)→Dω1,2q(M)whenever 1<p,q<∞.