The L p -L q 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 & ouml;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.