积域上一类沿曲线的振荡积分在调幅函数空间上的有界性

Boundedness of Certain Oscillatory Integral Along Curves in Product Domain on Modulation Space

调和分析中的一个热点问题是研究沿子流形上的奇异积分算子在各种空间上的有界性,大量数学工作者都得到了丰富的结果。研究主要利用振荡积分估计方法和Fourier变换估计方法,将沿齐次曲线的振荡积分算子推广到了沿满足一定条件的一般曲线的振荡积分算子,得到了该算子在调幅函数空间上的有界性,从而推广了前人的一些结果。

A hot topic in harmonic analysis is to study the boundedness of singular integral operators along submanifolds in various spaces.In this paper,we mainly used oscillatory integral estimation method and Fourier trans-form estimation method to extend the oscillatory integral operator along homogeneous curves to the oscillatory inte-gral operator along a general curve satisfying certain conditions,and obtained the boundedness of the operator in the modulation space.Thus,some results of predecessors are generalized.