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2007 Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
Jorge Rivera-Noriega
Abstr. Appl. Anal. 2007: 1-13 (2007). DOI: 10.1155/2007/92354

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. "Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations." Abstr. Appl. Anal. 2007 1 - 13, 2007. https://doi.org/10.1155/2007/92354

Information

Published: 2007
First available in Project Euclid: 27 February 2008

zbMATH: 1157.35346
MathSciNet: MR2283966
Digital Object Identifier: 10.1155/2007/92354

Rights: Copyright © 2007 Hindawi

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