New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk

Fang, Zhong-Shan ; Zhou, Ze-Hua

Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 794-802

Résumé

We give some new characterizations for compactness of weighted composition operators $u{{C}_{\varphi }}$ acting on Bloch-type spaces in terms of the power of the components of $\varphi$ , where $\varphi$ is a holomorphic self-map of the polydisk ${{\mathbb{D}}^{n}}$ , thus generalizing the results obtained by Hyvärinen and Lindström in 2012.

Détail

DOI : 10.4153/CMB-2013-043-4

Mots-clés : 47B38, 47B33, 32A37, 45P05, 47G10, weighted composition operator, compactness, Bloch type spaces, polydisk, several complex variables

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