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

Jorge Rivera-Noriega

Abstract and Applied Analysis, 2007, vol. 2007, 1-13

Abstract:

We prove distributional inequalities that imply the comparability of the L p 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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:092354

DOI: 10.1155/2007/92354

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