加权调幅空间上振荡积分算子的有界性及其应用

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

摘要: 基于振荡积分算子在勒贝格空间及调幅空间上的有界性，利用函数分解和振荡积分估计，得到了某类振荡积分算子在指标更广的加权调幅空间上的有界性，并将其推广到高维的加权调幅空间上，也得到了此类振荡积分算子在乘积空间上的有界性.

Abstract: 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.