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

By Hongjie Dong, Doyoon Kim. 2016

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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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4d5926a321db90238d182037eacef869478a56e0