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

A well-known theorem of K. Zhu {6} asserts that, for 2 ≤ p <∞, the Hankel operators Hf and Hf on the Bergman space L²ₐ(Bₙ,dV) of the unit ball belong to the Schatten class Cₚ if and only if the mean oscillation (f)(z) = \|f|²(z) - | f(z)|²\1/2 belongs to Lᵖ(Bₙ,(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.