Gleason’s Problems And Composition Operators On Some Holomorphic Function Spaces In C~n

In this thesis we mainly consider some problems on holomorphic function spaces in Cn. The thesis consists of four chapters.In Chapter1, we introduce the background of our studying problems and state our main results.In Chapter2, we prove that the Gleason’s problem (B,b,βu) or (Un. b,βu)is solvable for any fixed b∈B.In Chapter3, we discuss the boundedness and compactness conditions to a kind of integral operator Tφ,g on the Bloch type space. and give the necessary and sufficient conditionsIn Chapter4, we discuss the boundedness and compactness conditions of the weighted composition operator on some typical function spaces, and give the necessary and sufficient conditions by means of Finsler measure...