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April, 2002 Isometries of weighted Bergman-Privalov spaces on the unit ball of Cn
Yasuo MATSUGU, Sei-ichiro UEKI
J. Math. Soc. Japan 54(2): 341-347 (April, 2002). DOI: 10.2969/jmsj/05420341


Let B denote the unit ball in Cn, and v the normalized Lebesgue measure on B. For α>-1, define dvα(z)=Γ(n+α+1)/{Γ(n+1)Γ(α+1)}(1-|z|2)αdv(z), zB. Let H(B) denote the space of holomorphic functions in B. For p1, define

AN p να = f H B : f B log 1+ f p d να 1p < .

AN p να is an F-space with respect to the metric ρ fg f-g . In this paper we prove that every linear isometry T of AN p να into itself is of the form Tf= c fψ for all f AN p να , 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 να.


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Yasuo MATSUGU. Sei-ichiro UEKI. "Isometries of weighted Bergman-Privalov spaces on the unit ball of Cn." J. Math. Soc. Japan 54 (2) 341 - 347, April, 2002.


Published: April, 2002
First available in Project Euclid: 9 June 2008

zbMATH: 1027.32012
MathSciNet: MR1883522
Digital Object Identifier: 10.2969/jmsj/05420341

Primary: 32A37
Secondary: ‎32A36‎ , 32A38

Keywords: Bergman spaces , F-algebras , other spaces of holomorphic functions

Rights: Copyright © 2002 Mathematical Society of Japan


Vol.54 • No. 2 • April, 2002
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