On the Schatten class membership of Hankel operators on the unit ball

A well-known theorem of K. Zhu [7] asserts that, for 2 less than or equal to p < infinity, the Hankel operators H-f and H-(f)over bar on the Bergman space L-a(2)(B-n, dV) of the unit ball belong to the Schatten class C-p if and only if the mean oscillation MO(f)(z) = {(\f\(2))over tilde(z)-\(f)over tilde (z)\(2)}(1/2) belongs to L-p(B-n, 1-\z\(2))(-n-1)dV(z)). It is well known that, for trivial reasons, this theorem cannot be extended to the case p less than or equal to 2n/(n+1). This paper fills the gap between 2n/(n+1) and 2. More precisely, we prove that, when 2n/(n+1) < p < 2, the same theorem holds true.