Volterra Composition Operator From The Minimal M(o|¨)bius Invariant Space Into The Bloch Space

In this thesis we mainly study the boundedness and compactness of the Volterra composition operators from the minimal Mobius invariant space B1 into the Bloch s-pace.We have obtained the necessary and sufficient condition for the boundedness and compactness of the operators Ig,?:B1?B and Vg,? B1?B.And we obtained the necessary and sufficient condition for the boundedness and compactness of the operators Ig?:B1?B and Vg?:B1?B.In chapter 1,we give some related research background of the minimal Mobius invariant space B1 and Bloch space B and Volterra composition operators,and give some basic concepts and notations.At last,we show the significance of the research work.In chapter 2,we discuss the necessary and sufficient condition of the boundedness and compactness of the Volterra composition operator Ig,? from the minimal Mobius invariant space B1 into the Bloch space B and the little Bloch space B0.In chapter 3,we characterize the necessary and sufficient condition of the bound-edness and compactness of the Volterra composition operator Vg,? from the minimal Mobius invariant space B1 into the Bloch space B and the little Bloch space B0.In chapter 4,we characterize the necessary and sufficient condition of the bound-edness and compactness of the Volterra type composition operator Ig?(Vg?)from the minimal Mobius invariant space B1 into the Bloch space B and the little Bloch space B0.