Functions fixed by a weighted Berezin transform

초록

If f is M-harmonic and integrable with respect to a weighted radial measure v<inf>α</inf> over the unit ball B<inf>n</inf> of ℂn, then ∫<inf>B<inf>n</inf></inf> (f ◦ψ) dv<inf>α</inf> = f (ψ(0)) for every ψ ∈ Aut(B<inf>n</inf>). Equivalently f is fixed by the weighted Berezin transform; T<inf>α</inf> f = f. In this paper, we find the necessary and sufficient condition such that the equation T<inf>α</inf>f = f has only M-harmonic solutions in L1(B<inf>n</inf>, v<inf>α</inf>). © Research India Publications.

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