摘要
The boundedness on weighted local Hardy spaces h<sup>1,p</sup><sub>w</sub> of the oscillatory singular integral Tf（x）=∫<sub>R</sub><sup>n</sup> e<sup>iQ（x,y）</sup>K（x,y）f（y）dy is considered when Q（x,y）=P（x-y）for some real-valued polynomial P with its degree not less than two.Also a sufficient and necessary condition on polynomial Q on R<sup>n</sup> × R<sup>n</sup> such that T maps h<sup>1,p</sup><sub>w</sub> to the weighted integrable function space L<sup>1</sup><sub>w</sub> is found.
The boundedness on weighted local Hardy spaces h<sup>1,p</sup><sub>w</sub> of the oscillatory singular integral Tf（x）=∫<sub>R</sub><sup>n</sup> e<sup>iQ（x,y）</sup>K（x,y）f（y）dy is considered when Q（x,y）=P（x-y）for some real-valued polynomial P with its degree not less than two.Also a sufficient and necessary condition on polynomial Q on R<sup>n</sup> × R<sup>n</sup> such that T maps h<sup>1,p</sup><sub>w</sub> to the weighted integrable function space L<sup>1</sup><sub>w</sub> is found.
基金
This author is partially supported by the National Science Foundation of China
Zhejiang Provincial Sciences Foundation of China
