The <italic>L</italic> <italic>p</italic> -<italic>L</italic> <italic>q</italic> compactness of commutators of oscillatory singular integrals.

We study the compactness of commutator of a locally integrable function and an oscillatory singular integral operator defined by a real-valued polynomial and a kernel function satisfying the H&#246;lder condition. We show that such a commutator is compact from L p {L^{p}} to L q {L^{q}} if and only if the locally integrable function is the sum of a constant and a function in certain Lebesgue space. [ABSTRACT FROM AUTHOR]