| In this thesis,we mainly study the boundedness and compactness of the general?ized composition operatorsCφg from weighted α-Bloch space into weighted β—Bloch space for any α>0,β>0.Some sufficient and necessary conditions for the bound-edness and compactness of the generalized composition operators Cφg:Blogα→ Blogβare obtained.Meanwhile,Some sufficient and necessary conditions for the boundedness and compactness of the generalized composition operators Cφg:Blog,0α→ Blog,0βare also obtained.In Chapter 1,Some related research background of the generalized composition operatorsCφg from weighted α-Bloch space into weighted β—Bloch space be intro-duced,and some basic concepts and notations are given.At last,the content and the significance of the research are showed.In Chapter 2,some lemma for the boundedness and compactness of the generalized composition operatorsCφg from weighted α—Bloch space into weightedβ—Bloch space and the generalized composition operatorsCφg from little weighted α-Bloch space into little weighted β—Bloch space are given.In Chapter 3,Some sufficient and necessary conditions for the boundedness and compactness of the generalized composition operatorsCφg from weighted α—Bloch space into weightedβ-Bloch space are obtained.Meanwhile,Some sufficient and nec-essary conditions for the boundedness and compactness of the generalized composition operatorsCφg from little weighted α—Bloch space into little weighted β—Bloch space are also obtained. |
