沿齐次曲线的振荡积分在Wiener共合空间上的有界性

Oscillatory integrals along homogeneous curves on Wiener amalgam space

定义沿齐次曲线的振荡积分Tn,α,βf(x)=p.v.∫-1^1f(x-Γθ(t))e^-2πi|t|^-β/t|t|^αdt,x∈R^n,α,β>0,其中Γθ(t)为R^n中的齐次曲线。本文考虑了上述算子在Wiener共合空间W(fL^p,L^q)(R^n)上的有界性。结果表明Wiener共合空间可看作经典Lebesgue空间的良好替代。

Let oscillatory integrals along homogeneous curves be defined by Tn,α,βf(x)=p.v.∫-1^1f(x-Γθ(t))e^-2πi|t|^-β/t|t|^αdt,x∈R^n,α,β>0,β>0,WhereΓθ(t)be homogeneous curves on R^n.The mainly task of this paper is to consider the boundedness of this integral operators on Wiener amalgam space W(fL^p,L^q)(R^n).The result shows that Wiener amalgam spaces are good substitutions for Lebesuge spaces.