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

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  • Jorge Rivera-Noriega

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.

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  • Jorge Rivera-Noriega, 2007. "Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations," Abstract and Applied Analysis, Hindawi, vol. 2007, pages 1-13, February.
    • Handle: RePEc:hin:jnlaaa:092354
    DOI: 10.1155/2007/92354
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