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On $ L_p$-estimates for elliptic and parabolic equations with $ A_p$ weights


Authors: Hongjie Dong and Doyoon Kim
Journal: Trans. Amer. Math. Soc. 370 (2018), 5081-5130
MSC (2010): Primary 35R05, 42B37, 35B45, 35K25, 35J48
DOI: https://doi.org/10.1090/tran/7161
Published electronically: February 26, 2018
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Abstract: We prove generalized Fefferman-Stein type theorems on sharp functions with $ A_p$ weights in spaces of homogeneous type with either finite or infinite underlying measure. We then apply these results to establish mixed-norm weighted $ L_p$-estimates for elliptic and parabolic equations/systems with (partially) BMO coefficients in regular or irregular domains.


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Additional Information

Hongjie Dong
Affiliation: Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02912
Email: hongjie_dong@brown.edu

Doyoon Kim
Affiliation: Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Republic of Korea
Email: doyoon_kim@korea.ac.kr

DOI: https://doi.org/10.1090/tran/7161
Received by editor(s): January 4, 2016
Received by editor(s) in revised form: November 11, 2016, and December 22, 2016
Published electronically: February 26, 2018
Additional Notes: The first author was partially supported by the NSF under agreement DMS-1056737.
The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054865).
Article copyright: © Copyright 2018 American Mathematical Society

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