Oscillatory integrals with variable Calderon-Zygmund kernel on vanishing generalized Morrey spaces

In this paper, the authors investigate the boundedness of the oscillatory singular integrals with variable CalderOn-Zygmund kernel on generalized Morrey spaces M-p,M-phi(R-n) and the vanishing generalized Morrey spaces VMp,phi(R-n). When 1 < p < infinity and (phi(1), phi(2)) satisfies some conditions, we show that the oscillatory singular integral operators T-lambda and T-lambda* are bounded from M-p,M-phi 1(R-n) to M-p,M-phi 2(R-n) and from VM(p,phi)1(R-n) to VMp,phi 2(R-n). Meanwhile, the corresponding result for the oscillatory singular integrals with standard CalderOn-Zygmund kernel are established.