Little Hankel Operators on the Weighted Bergman Space of the Unit Ball

Abstract

In this paper we mainly consider little Hankel operators with square-integrable symbols on the weighted Bergman spaces of the unit ball. We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that $SMO(f) ∈ L^{\frac{p}{2}}(B_n, dλ)$ and $2 ≤ p < ∞,$ which is very important to research the relation between Toeplitz operators and little Hankel operators.