AN ENDPOINT ESTIMATE FOR MAXIMAL MULTILINEAR SINGULAR INTEGRAL OPERATORS

A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives o...

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Bibliographic Details
Published inAnalysis in theory & applications Vol. 23; no. 4; pp. 307 - 314
Main Author Jiao, Yulan
Format Journal Article
LanguageEnglish
Published School of Sciences Information Engineering University Zhengzhou, 450001 P.R. China 01.12.2007
Subjects
估计
奇异积分算子
有界平均振荡
消失条件
maximal multilinear singular integral operator
bounded mean oscillation
vanishing condition
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Summary:A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.
Bibliography:32-1631/O1
O17
maximal multilinear singular integral operator, bounded mean oscillation,vanishing condition
ISSN:1672-4070
1573-8175
DOI:10.1007/s10496-007-0307-2