Composition operators on the polydisc induced by smooth symbols

초록

We study composition operators C-Phi on the Hardy spaces H-p and weighted Bergman spaces A(alpha)(p) of the polydisc D-n in C-n. When Phi is of class C-2 on (D-n) over bar, we show that C-Phi is bounded on H-p or A(alpha)(p) if and only if the Jacobian of Phi does not vanish on those points zeta on the distinguished boundary T-n such that Phi(zeta) is an element of T-n. Moreover, we show that if epsilon > 0 and if C-Phi : A(alpha)(p) -> A(alpha+1/2n-epsilon)(p), then C-Phi is bounded on A(alpha)(p). (c) 2008 Elsevier Inc. All rights reserved.

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