Composition operators on the polydisc induced by smooth symbols

Hyung Woon Koo, Michael Stessin, Kehe Zhu

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)2911-2925
Number of pages15
JournalJournal of Functional Analysis
Volume254
Issue number11
DOIs
Publication statusPublished - 2008 Jun 1

Fingerprint

Polydisk
Composition Operator
Weighted Bergman Space
Hardy Space
Vanish
If and only if
Class

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 journalArticle

Koo, Hyung Woon ; Stessin, Michael ; Zhu, Kehe. / Composition operators on the polydisc induced by smooth symbols. In: Journal of Functional Analysis. 2008 ; Vol. 254, No. 11. pp. 2911-2925.
@article{3eb4b160525c4de497c5ca67878dff2f,
title = "Composition operators on the polydisc induced by smooth symbols",
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.",
keywords = "Composition operator, Jacobian, Polydisc",
author = "Koo, {Hyung Woon} and Michael Stessin and Kehe Zhu",
year = "2008",
month = "6",
day = "1",
doi = "10.1016/j.jfa.2008.03.003",
language = "English",
volume = "254",
pages = "2911--2925",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "11",

}

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 -