Blasco, Oscar; Lindström, Mikael; Taskinen, Jari Bloch-to-BMOA compositions in several complex variables. (English) Zbl 1093.47025 Complex Variables, Theory Appl. 50, No. 14, 1061-1080 (2005). For a positive integer \(n\), let \(B_n\) denote the open unit ball in the complex Euclidean space \(\mathbb C^n\). For a holomorphic function \(\varphi:B_n\to B_m\), the paper studies the boundedness and compactness of the composition operator \[ C_\varphi:{\mathcal B}(B_m)\to BMOA(B_n), \] where \(\mathcal B\) is the Bloch space. The main result of the paper states that, under a mild condition on the regularity of \(\varphi\), the boundedness of \(C_\varphi\) above is equivalent to the measure \[ d\mu(z)={(1-| z| ^2)| Rf(z)| \over (1-| \varphi(z)| ^2)^2}\,dv(z) \] being a Carleson measure, where \(dv\) is the volume measure and \(Rf(z)\) is the radial derivative of \(f\) at \(z\). Reviewer: Kehe Zhu (Albany) Cited in 6 Documents MSC: 47B33 Linear composition operators 32A18 Bloch functions, normal functions of several complex variables 32A70 Functional analysis techniques applied to functions of several complex variables Keywords:composition operator; Bloch space; BMOA PDFBibTeX XMLCite \textit{O. Blasco} et al., Complex Variables, Theory Appl. 50, No. 14, 1061--1080 (2005; Zbl 1093.47025) Full Text: DOI