沿超曲面的强奇异积分算子在调幅空间上的有界性

Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (4): 959-967.

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Hypersingular Integrals along Hypersurface on Modulation Spaces

CHENG Mei-Fang¹, ZHANG Zhen-Qiu²

1.College of Mathematics and Computer Sciences, Anhui Normal University, Anhui Wuhu 241000;
2.School of Mathematical Sciences, Nankai University, Tianjin 300071

Received:2009-03-06 Revised:2010-05-11 Online:2010-07-25 Published:2010-07-25
Supported by:
国家自然科学基金(10671041, 10971039)、安徽省教育厅一般项目(KJ2008B244)和安徽师范大学青年科学基金(2007xqn50)资助

Abstract

Abstract:

Let
$$Tf(x,x_{n})={\rm p.v.}\int\frac{f(x-y,x_{n}-\gamma(y)){\rm e}^{-2\pi {\rm i}|y|^{-\beta}}\Omega(y)h(y)}{|y|^{n+\alpha-1}}{\rm d}y,
~~~x,y\in{{\Bbb R}}^{n-1}, x_{n}\in{\Bbb R}.$$ The purpose of this paper is to investigate the boundedness of such integral operators on general modulation spaces. Here the rough kernel $\Omega$ is in the $L^1(S^{n-2})$, $h(y)$ is a bounded radial fuction and $\gamma(y)$ is an appropriate hypersurface.

Key words: Hyper-singular integral, Modulation space, Hypersurface

CLC Number:

42B20

CHENG Mei-Fang, ZHANG Zhen-Qiu. Hypersingular Integrals along Hypersurface on Modulation Spaces[J].Acta mathematica scientia,Series A, 2010, 30(4): 959-967.

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References

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Hypersingular Integrals along Hypersurface on Modulation Spaces

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