Weighted boundedness of fractional oscillatory integral operators with non-convolution kernels and their commutators

Abstract

Boundedness of oscillatory integral operator is one of key problems in harmonic analysis. In this paper, we establish the boundedness for a class of fractional oscillatory integral operators with non-convolution kernels, due to Ricci and Stein, on weighted Lebesgue spaces. Particularly, we obtain the weighted boundedness of commutators generated by these operators and BMO functions by combining the methods of complex analysis and induction.