Weighted vector-valued estimates for a non-standard Calder\'on-Zygmund operator

@article{Hu2016WeightedVE,
  title={Weighted vector-valued estimates for a non-standard Calder\'on-Zygmund operator},
  author={G. Hu},
  journal={arXiv: Classical Analysis and ODEs},
  year={2016}
}
  • G. Hu
  • Published 2016
  • Mathematics
  • arXiv: Classical Analysis and ODEs
In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)\big)f(y){\rm d}y,$$ and the corresponding maximal operator $T_A^*$, where $\Omega$ is homogeneous of degree zero, has vanishing moment of order one, $A$ is a function in $\mathbb{R}^n$ such that $\nabla A\in {\rm BMO}(\mathbb{R}^n)$. By a pointwise estimate for $\|\{T_Af_k(x)\}\|_{l^q}$ and the… Expand
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  • G. Hu
  • Mathematics
  • Journal of the Australian Mathematical Society
  • 2019
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  • Mathematics, Physics
  • Proceedings of the Edinburgh Mathematical Society
  • 2019
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