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Compact composition operators on \(H^ p(B_ N)\). (English) Zbl 0585.47022

Let \(B_ N\) be the open unit ball in \(C^ N\) and let \(\Phi:B_ N\to B_ N\) be a holomorphic self-map of \(B_ N\). For a holomorphic function f on \(B_ N\) denote the composition \(f\circ \phi\) by \(C_{\phi}(f)\). In the paper under review the boundedness and respectively the compactness of the operator \(C_{\phi}\), called the composition operators induced by \(\phi\), on some Hardy space \(H_ p(B_ N)\), \(0<p<\infty\), are investigated.
Reviewer: V.Kvaratskhelia

MSC:

47B38 Linear operators on function spaces (general)
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
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