BMO, VMO and Hankel operators on the Bergman space of strongly pseudoconvex domains

AbstractFor bounded strongly pseudoconvex domains D with smooth boundary in Cn, we introduce a kind of “mean oscillation” in terms of the Kobayashi metric. For f ϵ L2(D), it is shown that if f has “bounded mean oscillation on D,” then the Hankel operators Hf and Hf from the Bergman space H2(D), consisting of all holomorphic L2 functions, into L2(D) are bounded; if f has “vanishing mean oscillation at the boundary of D,” then Hf and Hf are compact. For f ϵ H2(D), the conditions are also necessary