Weighted estimates for strongly singular integral operators with rough kernels

HUANG Wen-Li;TAO Xiang-Xing;LI Sheng-Hong

doi:10.1007/s10483-010-1310-z

Applied Mathematics and Mechanics >

2010 , Vol. 31 >Issue 6: 761 - 768

DOI: https://doi.org/10.1007/s10483-010-1310-z

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Weighted estimates for strongly singular integral operators with rough kernels

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1. Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China;
2. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China

Received date: 2009-11-05

Revised date: 2010-05-08

Online published: 2010-06-01

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Abstract

The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.

Key words： strongly singular integral operators; rough kernels; Ap weights

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HUANG Wen-Li;TAO Xiang-Xing;LI Sheng-Hong . Weighted estimates for strongly singular integral operators with rough kernels[J]. Applied Mathematics and Mechanics, 2010 , 31(6) : 761 -768 . DOI: 10.1007/s10483-010-1310-z

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