Area integral estimates for solutions and normalized adjoint solutions to nondivergence form elliptic equations

Abstract

We show that the L^p norms, 0< p<∞, of the nontangenital maximal function and area integral of solutions and normalized adjoint solutions to second order nondivergence form elliptic equations, are comparable when integrated on the boundary of a Lipschitz domain with respect to measures, which are respectively A_∞ with respect to the corresponding harmonic measure or normalized harmonic measure.