Some one-sided estimates for oscillatory singular integrals

Abstract

The purpose of this paper is to establish some one-sided estimates for oscillatory singular integrals. The boundedness of certain oscillatory singular integrals on weighted Hardy spaces H+1(w) is proved. It is here also shown that the H+1(w) theory of oscillatory singular integrals above cannot be extended to the case of H+q(w) when 0<q<1 and w∈Ap+, a wider weight class than the classical Muckenhoupt class. Furthermore, a criterion on the weighted Lp-boundedness of the oscillatory singular integral is given.