A BMO ESTIMATE FOR THE MULTILINEAR
SINGULAR INTEGRAL OPERATOR
Qihui Zhang
【期刊名称】《分析、理论与应用（英文版）》 【年(卷),期】2006(022)003
【摘要】The behavior on the space L∞((R)n) for the multilinear singular integral operator defined by TAf(x)=∫Rn Ω(x-y)/|x-y|n+1(A(x)-A(y)-(△)A(y)(x-y))f(y)dy is considered, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, A has derivatives of order one in BMO((R)n). It is proved that if Ω satisfies some minimum size condition and an L1-Dini type regularity condition, then for f ∈ L∞((R)n), TAf is either infinite almost everywhere or finite almost everywhere, and in the latter case, TAf ∈ BMO((R)n). 【总页数】12页(271-282)
【关键词】multilinear singular integral operator, L1-Dini type regularity condition
【作者】Qihui Zhang
【作者单位】Department of Applied Mathematics University of Information Engineering P. O. Box 1001-7410, Zhengzhou, 450002 P. R. China
【正文语种】中文 【中图分类】O1
A BMO ESTIMATE FOR THE MULTILINEAR SINGULAR INTEGRAL OPERATOR
