Abstract
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 [ M f , J ] is bounded or compact on L p 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 C n and finite type domains in C 2. In addition, it is shown that, in the case of the Bergman projection in a strictly pseudoconvex domain, the sufficient condition is also necessary.
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