Boundedness,Compactness And Schatten-p Class Of Hankel Operators On Doubling Fock Spaces

In this paper,IDA spaces of locally integrable functions whose integral distance to holomorphic function is finite and their geometric theory are studied.we characterize the boundedness and compactness of Hankel operators from the doubling Fock spaces F_φ~p to the doubling Lebesgue spaces F_φ~q for all possible 1≤p,q<∞ by(p,q)-Fock Carleson measures.Moreover,the Schatten-p class of Hankel operators on doubling Fock spaces F_φ~2 are all considered for 0<p<∞.In Chapter 1,we introduce the historical background and research status about boundedness,compactness and Schatten-p class of Hankel operators、doubling Fock spaces and main results of this thesis.In Chapter 2,we introduce an auxiliary operator and the unit decomposition to characterize the Hormander’s (?)-theory of doubling Fock spaces.In Chapter 3,we introduce IDA spaces and their geometric theory.In Chapter 4,we characterize the boundedness and compactness of Hankel operators from the doubling Fock spaces F_φ~p to the doubling Lebesgue spaces L_φ~q for all possible 1≤p,q<∞ by(p,q)-Fock Carleson measuresIn Chapter 5,we characterize the Schatten-p class of Hankel operators on doubling Fock spaces F_φ~2 for 0<p<∞.