| 王荣乾.一类多线性奇异积分算子的加权估计[J].数学研究及应用,2014,34(2):168~174 |
| 一类多线性奇异积分算子的加权估计 |
| Weighted Norm Inequalities for a Class of Multilinear Singular Integral Operators |
| 投稿时间：2013-01-16 修订日期：2013-07-09 |
| DOI：10.3770/j.issn:2095-2651.2014.02.006 |
| 中文关键词: 多线性奇异积分算子 加权不等式 sharp函数估计 BMO$(\mathbb{R}^n)$. |
| 英文关键词:multilinear singular integral operator weighted norm inequality sharp function estimate BMO. |
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| 中文摘要: |
| 本文考虑多线性奇异积分算子$$T_{A}f(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)(x-y)\big)f(y)\,dy$$的带一般权函数的加权$L^p$估计,其中$\Omega$是零阶齐次函数, 具有一阶消失矩且属于${\rm Lip}_{\gamma}(S^{n-1})$ ($\gamma\in (0,\,1]$),$A$的所有的一阶偏微商属于${\rm BMO}(\mathbb{R}^n)$. |
| 英文摘要: |
| In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by $$T_{A}f(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)(x-y)\big)f(y)\d y,$$ where $\Omega$ is homogeneous of degree zero, has vanishing moment of order one, and belongs to ${\rm Lip}_{\gamma}(S^{n-1})$ with $\gamma\in (0,\,1]$, $A$ has derivatives of order one in ${\rm BMO}(\mathbb{R}^n)$. |
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