Abstract and Applied Analysis
Volume 2007 (2007), Article ID 92354, 13 pages
Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
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 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.