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

Rivera-Noriega, Jorge
January 2007
Abstract & Applied Analysis;2007, p1
Academic Journal
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 log u, 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.


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