Isometries of weighted Bergman-Privalov spaces on the unit ball of C^n

概要

論文の詳細を見る
Let B denote the unit ball in \bm{C}n, 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), z∈ B. Let H(B) denote the space of holomorphic functions in B. For p≥q 1, define(\displaystyle AN)^{\bm{p}}(vα)={f∈ H(B):\left//f\right//≡[∈tB{log(1+|f|)}pdvα]1/p<∞}.(AN)p(vα) 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(vα) into itself is of the form Tf=c(f\circψ) for all f∈(AN)p(vα), 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 vα.
社団法人日本数学会の論文