Bloch Type Spaces And Q _{T, S} Space

The introduction of Bloch spaces continually enlarge the scope of the research of function space theory. The conclusions obtained are more extensive. This would give some impetus both to the development of this direction and to the research of some others related fields. QT.s spaces are the extended QT spaces. In this paper, we mainly make a research on the relationship of Bloch type spaces and QT.s spaces, and discuss the boundedness and compactness of several kinds of operators acting from Bloch type spaces to QT.s spaces.First, we separately research the relationship from Bloch spaces and μ-B spaces to QT.s spaces. We give the necessary and sufficient condition for one equivalent condition of Bloch spaces and QT.s spaces, and one contain relation of μ-B spaces and QT.s spaces.Second, we separately discuss the boundedness and compactness of integral type operators acting from Bα spaces to QT.s spaces, and Blogα spaces to QT.s spaces.At last, we investigate the boundedness of composition operators and Volterra type composition operator acting from Bloch type spaces to QT.s spaces, and give the necessary and sufficient condition.