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On $l_p$-estimates for elliptic and parabolic equations with $a_p$ weights

Hongjie Dong Brown University Doyoon Kim Korea University

Analysis of PDEs mathscidoc:2005.03001

Trans. Amer. Math. Soc., 370, (7), 5081–5130, 2018.7
We prove generalized Fefferman-Stein type theorems on sharp functions with Ap weights in spaces of homogeneous type with either finite or infinite underlying measure. We then apply these results to establish mixed-norm weighted Lp-estimates for elliptic and parabolic equations/systems with (partially) BMO coefficients in regular or irregular domains.
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@inproceedings{hongjie2018on,
  title={ON $L_p$-ESTIMATES FOR ELLIPTIC AND PARABOLIC EQUATIONS WITH $A_p$ WEIGHTS},
  author={Hongjie Dong, and Doyoon Kim},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200508012939971251665},
  booktitle={Trans. Amer. Math. Soc.},
  volume={370},
  number={7},
  pages={5081–5130},
  year={2018},
}
Hongjie Dong, and Doyoon Kim. ON $L_p$-ESTIMATES FOR ELLIPTIC AND PARABOLIC EQUATIONS WITH $A_p$ WEIGHTS. 2018. Vol. 370. In Trans. Amer. Math. Soc.. pp.5081–5130. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200508012939971251665.
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