Boundedness of oscillatory integral operators on weighted modulation spaces and their applications

Based on the boundedness of oscillatory integral operators on Lebesgue spaces and modulation spaces, using function decomposition and oscillatory integral estimation, the boundedness of certain oscillatory integral operators on weighted modulation spaces with wider indexe is obtained and the boundedness is extended to weighted modulation spaces with higher dimensions, and the boundedness of such oscillatory integral operators on product spaces is also obtained.