AN INVARIANT MEAN VALUE PROPERTY IN THE POLYDISC

摘要

In [AFR], the authors showed that: If f is a bounded function on an n-dimensional unit ball B_n is contained in C~n satisfying ∫_(B_n) f ○ ψ dm = f(ψ(0)) for every ψ ∈ Aut(B_n) (where m is the normalized Lebesgue measure) then f is M-harmonic. And if f ∈ L~1(B_n, m) satisfies (1), then f is M-harmonic if and only if n ≤ 11. In this paper, we answer the question of whether the similar phenomenon happens in the n-dimensional polydisc D~n.