A Weighted Weak Type Endpoint Estimate for the Multilinear Calder\'on-Zygmund Operators and Its Applications

DOI：10.3770/j.issn:1000-341X.2010.02.017

 作者 单位 彭国强 解放军信息工程大学信息工程学院应用数学系, 河南 郑州 450002

本文建立了关于Coifman 和 Meyer引入的有Calder\'on-Zygmund 核的多线性算子的加权弱型端点估计. 作为应用,考虑了某一极大算子$M_B$和任意权$w$, 得到了权$M_Bw$在加权的$L^{p_1}(\rn)\times\cdots\,\times L^{p_m}(\rn)$空间上的性质, 还得到了算子的双权估计.

A weighted weak type endpoint estimate is established for the $m$-linear operator with Calder\'on-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted $L^{p_1}(\rn)\times\cdots\times L^{p_m}(\rn)$ with weight $M_Bw$ for certain maximal operator $M_B$ and general weight $w$, and a two-weight weighted norm estimate for this operator, are obtained.