Isometries of weighted Bergman-Privalov spaces on the unit ball of \bm{C}<SUP>n</SUP>

• MATSUGU Yasuo

  Department of Mathematical Sciences Faculty of Science, Shinshu University

• UEKI Sei-ichiro

  Department of Mathematical Sciences Faculty of Science, Shinshu University

Bibliographic Information

Other Title

• Isometries of weighted Bergman-Privalov spaces on the unit ball of Cn

Abstract

Let B denote the unit ball in \bm{C}ⁿ, and v the normalized Lebesgue measure on B. For α>-1, define dv_α(z)=Γ(n+α+1)/{Γ(n+1)Γ(α+1)}(1-|z|²)^αdv(z), z∈ B. Let H(B) denote the space of holomorphic functions in B. For p≥q 1, define<br>(\displaystyle AN)^{\bm{p}}(v_α)={f∈ H(B):\left//f\right//≡[∈t_B{log(1+|f|)}^pdv_α]^1/p<∞}.<br>(AN)^p(v_α) is an F-space with respect to the metric ρ(f, g)≡\left//f-g\right//. In this paper we prove that every linear isometry T of (AN)^p(v_α) into itself is of the form Tf=c(f\circψ) for all f∈(AN)^p(v_α), where c is a complex number with |c|=1 and ψ is a holomorphic self-map of B which is measure-preserving with respect to the measure v_α.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 54 (2), 341-347, 2002

  The Mathematical Society of Japan

Keywords

• Bergman spaces
• other spaces of holomorphic functions
• F-algebras

Details

• CRID: 1390001205114377600
• NII Article ID: 10008204974
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/05420341
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 1883522
• NDL BIB ID: 6153492
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I6153492
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed