We study composition operators CΦ on the Hardy spaces Hp and weighted Bergman spaces Aαp of the polydisc Dn in Cn. When Φ is of class C2 on over(Dn, -), we show that CΦ is bounded on Hp or Aαp if and only if the Jacobian of Φ does not vanish on those points ζ on the distinguished boundary Tn such that Φ (ζ) ∈ Tn. Moreover, we show that if ε > 0 and if CΦ : Aαp → Aα + frac(1, 2 n) - εp, then CΦ is bounded on Aαp.
- Composition operator
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