On the Boundedness and Compactness of Operators of Hankel Type

Boundedness and compactness results are obtained for commutators of multiplication operators with a general class of integral operators J of a critical homogeneity which are modeled on the Bergman projection. It is shown that the commutator [Mf, J] is bounded or compact on Lp whenever the function ƒ is in an appropriately defined BMO or VMO space, respectively. Special cases of the general results include commutators with the Bergman projection in strictly pseudoconvex domains in Cn and finite type domains in C2. In addition, it is shown that, in the case of the Bergman projection in a strictly pseudoconvex domain, the sufficient condition is also necessary.