Abstract and Applied Analysis
Volume 2007 (2007), Article ID 92354, 13 pages
Research Article

Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations

Jorge Rivera-Noriega

Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col Chamilpa, Cuernavaca Mor CP 62209, Mexico

Received 26 June 2006; Accepted 18 December 2006

Academic Editor: Vesa Mustonen

Copyright © 2007 Jorge Rivera-Noriega. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove distributional inequalities that imply the comparability of the Lp norms of the multiplicative square function of u and the nontangential maximal function of logu, where u 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 u is a harmonic function is considered.