A Characterization of M-Harmonicity

Abstract

Abstract. If f is M-harmonic and integrable with respect to a weighted radial measure ν α over the unit ball B n of C n , thenEquivalently f is fixed by the weighted Berezin transform; T α f = f . In this paper, we show that if a function f defined on B n satisfies R(f • φ) ∈ L ∞ (B n ) for every φ ∈ Aut(B n ) and Sf = rf for some |r| = 1, where S is any convex combination of the iterations of T α s, then f is M-harmonic.