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

A well-known theorem of K. Zhu [7] asserts that, for 2 ≤ p < ∞, the Hankel operators H_f and H_f̄ on the Bergman space L_a²(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(z) - |f̃(z)|²}^1/2 belongs to L^p(B_n, (1 - |z|²)^-n-1dV(z)). It is well known that, for trivial reasons, this theorem cannot be extended to the case p ≤ 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.