| Weighted Norm Inequalities for a Class of Multilinear Singular Integral Operators |
| Received:January 16, 2013 Revised:July 09, 2013 |
| Key Words:
multilinear singular integral operator weighted norm inequality sharp function estimate BMO.
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| Abstract: |
| 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 ${\rm BMO}(\mathbb{R}^n)$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.02.006 |
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