各向异性Herz型Hardy空间上的振荡奇异积分算子

Oscillatory Singular Integral Operators on Anisotropic Herz-type Hardy Spaces

研究了振荡奇异积分算子T在各向异性Herz型Hardy空间上的有界性问题。当相函数P(x,y)满足▽yP(0,y)=0并且p,q满足一定条件时,利用原子分解定理,证明了这类算子T是从HKq,αp到Kq,αp上的有界算子。这一结论丰富了各向异性Herz型Hardy空间上算子有界性理论。

The boundedness of the oscillatory singnlar integrals aperators on anisotropic Herz-type Hardy spaces is considered. Basing on the atomic decompositions. When polynomial phases provided △↓3P（O,y）=0 and p,q meet some certain conditions, the oscillatory singnlar integrals operators are bounded from anisotropic Herz-type Hardy spaces to anisotropic Herz spaces. This conclusion enriches the theories of boundedness of the oscillatory singular integrals operators on anisotropic Herz-type Hardy spaces.