Geodesic
Weighted composition operators between Bloch-type spaces in the polydisc
Sbornik. Mathematics, Tome 201 (2010) no. 2, pp. 289-319

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For $p>0$, let $\mathscr B^p(\mathbb D^n)$ denote the $p$-Bloch space on the unit polydisc $\mathbb D^n$ of $\mathbb C^n$ and $\varphi(z)=(\varphi_1(z),\dots,\varphi_n(z))$ a holomorphic self-map of $\mathbb D^n$. We investigate the boundedness and compactness of the weighted composition $uC_\varphi f(z)=u(z)f(\varphi(z))$ between $p$-Bloch space $\mathscr B^p(\mathbb D^n)$ (little $p$-Bloch space $\mathscr B^p_0(\mathbb D^n)$) and $q$-Bloch space $\mathscr B^q(\mathbb D^n)$ (little $q$-Bloch space $\mathscr B^q_0(\mathbb D^n)$). The most important result in the paper is that conditions for the compactness are different for the cases $p\in(0,1)$ and $p\geqslant1$, unlike for the case of the weighted operators on the unit disc. Bibliography: 32 titles.
Keywords: polydisc, weighted composition operator, boundedness, compactness.
Mots-clés : Bloch-type spaces 
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     title = {Weighted composition operators between {Bloch-type} spaces in the polydisc},
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S. Stević; R. Chen; Z. Zhou. Weighted composition operators between Bloch-type spaces in the polydisc. Sbornik. Mathematics, Tome 201 (2010) no. 2, pp. 289-319. http://geodesic.mathdoc.fr/item/SM_2010_201_2_a4/