一类振荡奇异积分算子在加权Herz空间的有界性

Boundedness of a Class of Oscillatory Singular Integral Operators on Weighted Herz Spaces

对于一类具μ-Calderón-Zygmund核的振荡奇异积分算子,已经得到了它的Lp(Rn)(1<p<∞)有界性,并且利用权函数的性质,又证明了它的加权Lp有界结果。这里借助于Herz空间的分解理论,证明了此类推广的具-μCalderón-Zygmund核的振荡奇异积分算子在非齐次加权Herz空间的有界性。

The boundedness of a class of oscillatory singular integral with μ-Calderón-Zygmund kernel on Lp（Rn）（1〈p〈∞） was obtained. And by the property of weighted function, it was also obtained the weighted boundedness. The boundedness of the oscillatory singular integral with μ-Calderón-Zygmund kernel is proved using the decomposition theory of the Herz space in the inhomogeneous weighted Herz space.