We introduce some
operators on the Bergman space A2 on the unit ball that generalize the
classical (big) Hankel operator. For such operators we prove boundedness,
compactness, and Schatten-ideal property criteria. These extend known results.
These new operators are defined in terms of a symbol. We prove in particular
that for 2 ≤ p < ∞, these operators belong to the Schatten ideal Sp if and
only if the symbol f is in the Besov space Bp. We also give several different
characterizations of the norm on the Besov spaces Bp. In particular we prove that the
Besov spaces are the mean oscillation spaces in the Bergman metric, for
1 ≤ p < ∞.
