Oscillatory integrals with variable Calderón-Zygmund kernel on generalized weighted Morrey spaces

Abstract

In this paper, we investigate the boundedness of the oscillatory singular integrals with variable Calderón-Zygmund kernel on the generalized weighted Morrey spaces Mp,?(w). When w the weights are in the Muckenhoupt class Ap, 1 < p < ? and (?1, ?2, w) satisfies some conditions, we show that the oscillatory singular integral operators T? and T??are bounded from Mp,?1 (w) to Mp,?2 (w). Meanwhile, the corresponding result for the oscillatory singular integrals with standard Calderón-Zygmund kernel are established. © 2022, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.