沿曲线的震荡积分在调幅函数空间上的有界性

Boundedness of the Oscillatory Integrals Along Curves on Modulation Space

对R^2上沿曲线(t,γ(t))的震荡积分算子T_(α,β)f(x,y)=∫_Rf(x-t,y-γ(t))e^(-i︱t︱β-1)t︱t︱~αdt进行研究,其中γ(t)=︱t︱~k或γ(t)=sgn(t)︱t︱~k.若对α,β进行适当的限制且k=0,1,2,则T_(α,β)在M_s^(p,q)上有界,其中1≤p≤∞,0<q≤∞且s∈R.

In this study, the oscillatory integral operator T_（α,β）f（x,y）=∫_Rf（x-t,y-γ（t））e^-i︱t︱β-1t︱t︱^αdt along the chive （t,γ（t）） in the two dimension space R^2 was studied, where γ（t）=︱t︱^k or γ（t）=sgn（t）︱t︱^k.If α,β satisfied some conditions and k =0, 1, 2, then operator Tα,β was bounded on Ms^p＋q for 1≤p≤∞,0〈q≤∞ and s∈R.