In this paper, function spaces Q p (B) and Q p,0 (B), associated with the Green's function, are defined and studied for the unit ball B of C n . We prove that Q p (B) and Q p,0 (B) are Möbius invariant Banach spaces and that Q p (B) = Bloch(B), Q p,0 (B) = B 0 (B) (the little Bloch space) when 1 < p < n/(n − 1), Q 1 = BMOA(∂B) and Q 1,0 (B) = VMOA(∂B). This fact makes it possible for us to deal with BMOA and Bloch space in the same way. And we give necessary and sufficient conditions on boundedness (and compactness) of the Hankel operator with antiholomorphic symbols relative to Q p (B) (and Q p,0 (B)). Moreover, other properties about the above spaces and |ϕ z (w)|, ϕ z (w) ∈ Aut(B), are obtained.

In this paper we prove that, in the unit ball B of C", a holomorphic function f is in the Bergman space LP(B), 0 < p < 00, if and only ifwhere V and A denote the invariant gradient and invariant measure on B, respectively. Further, 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(aB) functions in the unit ball.

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