AN INTEGRAL-TYPE OPERATOR FROM BLOCH SPACES TO Q(p) SPACES IN THE UNIT BALL

作者：Li Songxiao^*

来源：Mathematical Inequalities & Applications, 2012, 15(4): 959-972.

DOI：10.7153/mia-15-82

• Composition operator
• integral-type operator
• Bloch space
• Q(p) space

Let H(B) denote the space of all holomorphic functions on the unit ball B of C-n. Let alpha > 0, f is an element of H(B) with homogeneous expansion f = Sigma(infinity)(k=0) f(k). The fractional derivative D(alpha)f is defined as
D(alpha)f (z) = Sigma(infinity)(k=0) (k+1)(alpha) f(k)(z).
Let phi be a holomorphic self-map of B and g is an element of H(B) such that g(0) = 0. In this paper we consider the following integral-type operator
D-phi,g(alpha) f(z) = integral(1)(0) D(alpha)f(phi(tz))g(tz)dt/t, f is an element of H(B).
The boundedness of the operator D-phi,g(alpha) from the Bloch space to the spaces Q(p) and Q(p,0) are investigated. In particular, the boundedness and compactness of the operator D-phi,g(1) on the Bloch spaces are completely characterized.

• 出版日期2012-10
• 单位嘉应学院