Mingming Cao: Absolute Continuity of elliptic measure in 1-sided NTA domains satisfying CDC

Let Ω subset R^n+1, n less or equal 2 be a 1-sided NTA domain satisfying CDC. Let L_0 u = -div(A_0∇u). Lu = -div(A_0∇u) be two real uniformly elliptic operators in Ω, and write ω_L_0, ω_L for the respective associated elliptic measures. We establish the equivalence between the following: (i) ω_L Element A_infinity(ω_L_0). (ii) L is L^p(ω_L_0) solvable, (iii) bounded null solutions of L satisfy Carleson measure estimates with respect to ω_L_0, (iv) S less than N (i.e. the conical square function is controlled by the non-tangential maximal function) L^q (ω_L_0) for any null solution of L and (v) L is BMO(ω_L_0)-solvable.