CHARACTERIZATIONS OF BERGMAN SPACES AND BLOCH SPACE IN THE UNIT BALL OF C(N)

In this paper we prove that, in the unit bait B of C-n, a holomorphic function f is in the Bergman space L(a)(p)(B), 0 < p < infinity, if an d only if integral(B)\<(del)over tilde>f(z)\(2)\f(z)\(p-2)(1-\z\(2))(n +1)d lambda(z) < infinity, where <(del)over tilde> and lambda denote t he invariant gradient and invariant measure on B, respectively. Furthe r, we give some characterizations of Bloch functions in the unit ball B, including an exponential decay characterization of Bloch functions. We also give the analogous results for BMOA(partial derivative B) fun ctions in the unit ball.