Generalized integration operators between Bloch-type spaces and \(F(p,q,s)\) spaces. (English) Zbl 1295.47046

He, Zhong Hua; Cao, Guangfu

Taiwanese J. Math. 17, No. 4, 1211-1225 (2013).

Let \(H({\mathbb D})\) be the space of all holomorphic functions on the unit disk \(\mathbb D\) in the complex plane. Let \(\varphi\in H({\mathbb D})\), \(\varphi:{\mathbb D}\to {\mathbb D}\), \(n\) be a positive integer, \(g\in H({\mathbb D})\). The authors investigate operators of the form \[ (I_{g,\varphi}^{(n)}f)(z) = \int_{0}^{z}f^{(n)}(\varphi(\zeta))g(\zeta)\,d\zeta,\quad z\in {\mathbb D}, \] between Bloch-type spaces and \(F(p,q,s)\)-spaces. They obtain necessary and sufficient conditions for boundedness and compactness of these operators and two-sided norm estimates in the case of boundedness.

Reviewer: Vladimir S. Pilidi (Rostov-na-Donu)

MSC:

47G10	Integral operators
30H30	Bloch spaces
30H99	Spaces and algebras of analytic functions of one complex variable
47A30	Norms (inequalities, more than one norm, etc.) of linear operators

Keywords:

generalized integration operator; Bloch-type space; \(F(p,q,s)\)-space