某类沿曲面的强奇异积分算子在调幅函数空间上的有界性

Boundedness of Certain Hyper Singular Integral Operator Along Surface on Modulation Space

假设β1>α1>0,β2>α2>0。文章对如下定义的强奇异积分算子Hα,βf(x,y,z)=∫Q^2f(x-t,y-s,z-γ(t)h(s))e^-2πit■/t^1+α1s^1+α2dtds进行了讨论,其中Q^2=[0,1]^2,γ(t),h(s)满足某些适当的条件。利用振荡积分估计,得到当β1>3α1>0且β2>3α2>0时,算子Hα,β在调幅函数空间M^p,q(R^3)上有界,这里1≤p≤∞,0<q≤∞。

Supposeβ1>α1>0,β2>α2>0.In this paper,the hyper singular integral operator defined byHα,βf(x,y,z)=∫Q^2f(x-t,y-s,z-γ(t)h(s))e^-2πit■/t^1+α1s^1+α2dtds,where Q^2=[0,1]^2andγ(t),h(s)satisfy the appropriate conditions.With the oscillatory integral estimation,it is obtained that ifβ1>3α1>0 andβ2>3α2>0,then the operatoris Hα,βbounded on M^p,q(R^3)for 1≤p≤∞,0<q≤∞.