Lp boundedness of Carleson type maximal operators  with nonsmooth kernels

DING Yong; LIU Honghai

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Lp boundedness of Carleson type maximal operators with nonsmooth kernels

DING Yong 1,LIU Honghai 2

1.School of Mathematical Sciences, Beijing Normal University

2.School of Mathematics and InformationScience, Henan Polytechnic University

*Correspondence author

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Funding: Specialized Research Fund for the Doctoral Program of Higher Education （No.20090003110018）, National Natural Science Foundation of China （No.10931001）

Opened online:19 July 2011

Accepted by: none

Citation: DING Yong,LIU Honghai.Lp boundedness of Carleson type maximal operators with nonsmooth kernels[OL]. [19 July 2011] http://en.paper.edu.cn/en_releasepaper/content/4435357

Stein and Wainger have proved that Carleson type maximal operators is Lp bounded, where the phase function P(y) is polynomial without linear term and singular kernel K is smooth. In this artical, authors consider another kind of Carleson type maximal operators, where the phase function is P(|y|), P(t) is a polynomial on R without linear term, K(y)=Ω(y)/|y|n, Ω∈H1(Sn-1). They obtain the Lp boundedness for this kind of Carleson type maximal operators by Stein-Wainger's TT* argument and Calderon-Zygmund's rotation method.

Keywords:Fundamental Mathematics; Carleson type maximal operators; Singular integrals; Oscillatory integrals; Rough kernel

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