多线性Calder\'on-Zygmund算子的加权弱型端点估计及其应用

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

中文关键词:  多线性Calder\'on-Zygmund算子  极大算子  加权不等式  插值.

英文关键词:multilinear Calder\'on-Zygmund operator  maximal operator  weighted norm inequality  interpolation.

中文摘要:

      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.

英文摘要:

      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.