Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 2911-2925 |
| Number of pages | 15 |
| Journal | Journal of Functional Analysis |
| Volume | 254 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2008 Jun 1 |
Fingerprint
Keywords
- Composition operator
- Jacobian
- Polydisc
ASJC Scopus subject areas
- Analysis
Cite this
Composition operators on the polydisc induced by smooth symbols. / Koo, Hyung Woon; Stessin, Michael; Zhu, Kehe.
In: Journal of Functional Analysis, Vol. 254, No. 11, 01.06.2008, p. 2911-2925.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Composition operators on the polydisc induced by smooth symbols
AU - Koo, Hyung Woon
AU - Stessin, Michael
AU - Zhu, Kehe
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
UR - http://www.scopus.com/inward/record.url?scp=41949106537&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=41949106537&partnerID=8YFLogxK
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 -