We prove distributional inequalities that imply the comparability of the norms of the multiplicative square function of and the nontangential maximal function of , where is a positive solution of a nondivergence elliptic equation. We also give criteria for singularity and mutual absolute continuity with respect to harmonic measure of any Borel measure defined on a Lipschitz domain based on these distributional inequalities. This extends recent work of M. González and A. Nicolau where the term multiplicative square functions is introduced and where the case when is a harmonic function is considered.
"Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations." Abstr. Appl. Anal. 2007 1 - 13, 2007. https://doi.org/10.1155/2007/92354