Hankel operators in the Bergman space and Schatten p-classes:: The case 1<p<2

K. Zhu proved in Amer. J. Math. 113 (1991), 147-167, that, for 2 less than or equal to p < <infinity>, the Hankel operators H-f and H-(f) over bar on the Bergman space belong to the Schatten class C-p if and only if the mean oscillation MO(f)(z) = {<(<vertical bar>f \ (2))over tilde>(z) - \(f) over tilde (z)\ (2)}(1/2) belongs to L-p (D,(1 - \z \ (2))(-2)dA(z)). In this paper we prove that the same result also holds when 1 < p < 2.