We show that if $f in L^{infty}(D^n)$ satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of Berezin operator, then f is n-harmonic. And we give some remarks and a conjecture on the space $$ M_2 = {f in L^2(D^2, m imes m)$mid$Bf = f}. $$</TEX>