This article is devoted to studying the decomposition of functions of Qp spaces, which unify Bloch space and BMOA space in the scale of p. A decomposition theorem is established for Qp spaces with small scale p, n-1/n〈 p ≤ 1 by means of p-Carleson measure and the Bergman metric on the unit ball of Cn. At the same time, a decomposition theorem for Qp,O spaces is given as well.
In this paper, we prove that： if M is a family which has convexity radius, then the convexity radius for M and the second order item coefficients of every mapping in M are closely related to each other. As an application, we show that the convexity radius of starlike mappings r（S＊） 〈 2-3～（1/2）.
In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.
We find a lower bound for the essential norm of the difference of two composition operators acting on H 2（BN ） or As2 （BN ） （s 1）. This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005.
