α-Bloch Spaces And Composition Operators On The Unit Ball

In this thesis, we investigate composition operators and multiplication operators betweenα-Bloch spaces, and weighted composition operators of H~∞intoα-Bloch spaces on the unit ball.First, we introduce a new metric F_z~α(v), and then, the equivalent norms ofα-Bloch functions on the unit ball are given, which extend the result of Timoney for Bloch functions on the unit ball. Meanwhile, we give equivalent definitions of the littleα-Bloch functions on the unit ball.Second, by using the metric F_z~α(v), we characterize the boundedness and compactness of composition operators betweenα-Bloch spaces on the unit ball and obtain necessary and sufficient conditions of boundedness and compactness. We also establish necessary and sufficient conditions of the boundedness and compactness of weighted composition operators of H~∞intoα-Bloch spaces on the unit ball, which improve the result of S. X. Li and S. Stevic.At last, the boundedness from below of multiplication operators betweenα-Bloch spaces of the unit ball is studied completely.