In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on Lipschitz domains. Also, we give their application for the harmonic function defined in bounded Lipschitz domains.
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
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）&...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.展开更多
The authors show that the Cauchy integral operator is bounded from Hωp(R1) to hωp(R1) (the weighted local Hardy space). To prove the results, a kind of generalized atoms is introduced and a variant of weighted "...The authors show that the Cauchy integral operator is bounded from Hωp(R1) to hωp(R1) (the weighted local Hardy space). To prove the results, a kind of generalized atoms is introduced and a variant of weighted "Tb theorem" is considered.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10377108)the Natural Science Foundation of Guangdong Province (No. 031495), China
文摘In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on Lipschitz domains. Also, we give their application for the harmonic function defined in bounded Lipschitz domains.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
基金This author is partially supported by the National Science Foundation of ChinaZhejiang Provincial Sciences Foundation of China
文摘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supported by the National Natural Science Foundation of China(Nos.10571156,10871173,10931001)the Zhejiang Provincial Natural Science Foundation of China(No.Y606117)the Science Foundation of Education Department of Zhejiang Province(No.Y200803879)
文摘The authors show that the Cauchy integral operator is bounded from Hωp(R1) to hωp(R1) (the weighted local Hardy space). To prove the results, a kind of generalized atoms is introduced and a variant of weighted "Tb theorem" is considered.
