Composition operators on Hardy space in several complex variables (Q1093875)

Let B denote the unit disc of \({\mathbb{C}}^ n\) and let \(\omega\) be an analytic map with \(\omega\) (B)\(\subset B\). The equation \(C_{\omega}f=f\circ \omega\) defines a composition operator \(C_{\omega}\) on the Hardy space \(H^ 2(B)\). The author provides conditions for \(C_{\omega}\) to be invertible, compact, and of trace class [cf. also \textit{J. M. Shapiro}, Ann. Math., II. Ser. 125, 375-404 (1987)].