| 焦玉兰,陈正刚.多线性Calder\'on-Zygmund算子的多权弱型估计[J].数学研究及应用,2011,31(5):855~862 |
| 多线性Calder\'on-Zygmund算子的多权弱型估计 |
| Multi-weight, Weighted Weak Type Estimates for the Multilinear Calder\'{o}n-Zygmund Operators |
| 投稿时间：2010-01-21 修订日期：2010-10-03 |
| DOI：10.3770/j.issn:1000-341X.2011.05.011 |
| 中文关键词: 多线性Calder\'{o}n-Zygmund算子 权模不等式 Calder\'on-Zygmund分解 极大算子. |
| 英文关键词:multilinear Calder\'{o}n-Zygmund operator weighted norm inequalities Calder\'on-Zygmund decomposition maximal operators. |
| 基金项目:国家自然科学基金 (Grant No.10971228). |
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| 中文摘要: |
| 设$m$是一个自然数, $T$是$m$-线性Calder\'on-Zygmund算子, $u,\,v_1,...,\,v_m$是权函数. 本文给出权函数对$(u,\,v_k)$ ($1\leq k\leq m$)使得算子$T$是$L^{p_1}(\rn,\,v_1)\times...\times L^{p_m}(\rn,\,v_m)$到$L^{p,\,\infty}(\rn,\,u)$有界的一个充分条件. |
| 英文摘要: |
| Let $m$ be an integer and $T$ be an $m$-linear Calder\'on-Zygmund operator, $u,\,v_1,...,\,v_m$ be weights. In this paper, the authors give some sufficient conditions on the weights $(u,\,v_k)$ with $1\leq k\leq m$, such that $T$ is bounded from $L^{p_1}(\rn,\,v_1)\times\cdots\times L^{p_m}(\rn,\,v_m)$ to $L^{p,\,\infty}(\rn,\,u)$. |
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