Zeng, Hong-Gang; Zhou, Ze-Hua An estimate of the essential norm of a composition operator from \(F(p,q,s)\) to \(\mathcal B^\alpha \) in the unit ball. (English) Zbl 1191.47033 J. Inequal. Appl. 2010, Article ID 132970, 22 p. (2010). Summary: Let \(B_n\) be the unit ball of \(\mathbb C^{n}\) and \(\varphi =(\varphi_{1},\dots ,\varphi_{n})\) a holomorphic self-map of \(B_n\). Let \(0<p,s<\infty\), \(-n-1<q<\infty\), \(q+s>-1\), \(\alpha >0\), and let \(C_{\varphi}\) be the composition operator between the space \(F(p,q,s)\) and \(\alpha \)-Bloch space \(\mathcal B^{\alpha}\) induced by \(\varphi \). This paper gives an estimate of the essential norm of \(C_{\varphi}\). As a consequence, a necessary and sufficient condition for the composition operator \(C_{\varphi}\) to be compact from \(F(p,q,s)\) to \(\mathcal B^{\alpha}\) is obtained. Cited in 6 Documents MSC: 47B33 Linear composition operators 46E15 Banach spaces of continuous, differentiable or analytic functions 32A18 Bloch functions, normal functions of several complex variables PDFBibTeX XMLCite \textit{H.-G. Zeng} and \textit{Z.-H. Zhou}, J. Inequal. Appl. 2010, Article ID 132970, 22 p. (2010; Zbl 1191.47033) Full Text: DOI References: [1] doi:10.1216/rmjm/1021477265 · Zbl 0978.32002 · doi:10.1216/rmjm/1021477265 [2] doi:10.1112/blms/12.4.241 · Zbl 0416.32010 · doi:10.1112/blms/12.4.241 [3] doi:10.1007/s10114-007-0993-x · Zbl 1149.47014 · doi:10.1007/s10114-007-0993-x [4] doi:10.2307/2154848 · Zbl 0826.47023 · doi:10.2307/2154848 [5] doi:10.1007/s101149900028 · Zbl 0967.32007 · doi:10.1007/s101149900028 [7] doi:10.1307/mmj/1028575740 · Zbl 1044.47021 · doi:10.1307/mmj/1028575740 [8] doi:10.1007/s00020-002-1203-y · Zbl 1065.47027 · doi:10.1007/s00020-002-1203-y [9] doi:10.2140/pjm.1999.188.339 · Zbl 0932.30034 · doi:10.2140/pjm.1999.188.339 [12] doi:10.1142/S0129167X08004984 · Zbl 1163.47021 · doi:10.1142/S0129167X08004984 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.