Composition operators on the polydisc induced by smooth symbols

Hyungwoon Koo; Michael Stessin; Kehe Zhu

doi:10.1016/j.jfa.2008.03.003

Composition operators on the polydisc induced by smooth symbols

Hyungwoon Koo, Michael Stessin, Kehe Zhu

Department of Mathematics

Research output: Contribution to journal › Article

6 Citations (Scopus)

Abstract

We study composition operators C_Φ on the Hardy spaces H^p and weighted Bergman spaces A_α^p of the polydisc Dⁿ in Cⁿ. When Φ is of class C² on over(Dⁿ, -), we show that C_Φ is bounded on H^p or A_α^p 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 C_Φ : A_α^p → A_{α + frac(1, 2 n) - ε}^p, then C_Φ is bounded on A_α^p.

Original language	English
Pages (from-to)	2911-2925
Number of pages	15
Journal	Journal of Functional Analysis
Volume	254
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2008.03.003
Publication status	Published - 2008 Jun 1

Keywords

Composition operator
Jacobian
Polydisc

ASJC Scopus subject areas

Analysis

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Koo, H., Stessin, M., & Zhu, K. (2008). Composition operators on the polydisc induced by smooth symbols. Journal of Functional Analysis, 254(11), 2911-2925. https://doi.org/10.1016/j.jfa.2008.03.003

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AU - Zhu, Kehe

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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.

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