A CHARACTERIZATION OF M-HARMONICITY

초록

If f is M-harmonic and integrable with respect to a weighted radial measure nu(alpha) over the unit ball B(n) of C(n), then integral(Bn) (f o psi) d nu(alpha) = f(psi(0)) for every psi is an element of Aut(B(n)). Equivalently f is fixed by the weighted Berezin transform; T(alpha)f = f. In this paper, we show that if a function f defined on B(n) satisfies R(f o phi) is an element of L(infinity)(B(n)) for every phi is an element of Aut(B(n)) and Sf = r f for some vertical bar r vertical bar = 1, where S is any convex combination of the iterations of T(alpha)'s, then f is M-harmonic.

키워드