TY - JOUR
T1 - Composition operators on the polydisc induced by smooth symbols
AU - Koo, Hyungwoon
AU - Stessin, Michael
AU - Zhu, Kehe
N1 - Funding Information:
✩ H. Koo is partially supported by SBS and K. Zhu is partially supported by NSF. * Corresponding author. E-mail addresses: koohw@korea.ac.kr (H. Koo), stessin@math.albany.edu (M. Stessin), kzhu@math.albany.edu (K. Zhu).
PY - 2008/6/1
Y1 - 2008/6/1
N2 - 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.
AB - 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.
KW - Composition operator
KW - Jacobian
KW - Polydisc
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U2 - 10.1016/j.jfa.2008.03.003
DO - 10.1016/j.jfa.2008.03.003
M3 - Article
AN - SCOPUS:41949106537
VL - 254
SP - 2911
EP - 2925
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 11
ER -