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

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.

A solvability result added

References in corpus (1)

• Neumann problem for non-divergence elliptic and parabolic equations with BMO${}_x$ coefficients in weighted Sobolev spaces

Cited by in corpus (3)

• An lp-boundedness of stochastic singular integral operators and its application to spdes
• Weighted $L_q$-estimates for stationary Stokes system with partially BMO coefficients
• $L_p$-estimates for time fractional parabolic equations with coefficients measurable in time