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

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

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 logu, where u is a positive solution of a nondivergence elliptic equation. We also give criteria for singularity and mutual absolute...

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Main Author: Jorge Rivera-Noriega
Format: Article
Language:English
Published: Hindawi Limited 2007-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2007/92354
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spelling doaj-0737c8ee7ae945228410bb34e58217092020-11-25T01:44:06ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/9235492354Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic EquationsJorge Rivera-Noriega0Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col Chamilpa, Cuernavaca Mor CP 62209, MexicoWe prove distributional inequalities that imply the comparability of the Lp norms of the multiplicative square function of u and the nontangential maximal function of logu, 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.http://dx.doi.org/10.1155/2007/92354
collection DOAJ
language English
format Article
sources DOAJ
author Jorge Rivera-Noriega
spellingShingle Jorge Rivera-Noriega
Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
Abstract and Applied Analysis
author_facet Jorge Rivera-Noriega
author_sort Jorge Rivera-Noriega
title Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
title_short Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
title_full Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
title_fullStr Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
title_full_unstemmed Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
title_sort estimates for the multiplicative square function of solutions to nondivergence elliptic equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2007-01-01
description 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 logu, 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.
url http://dx.doi.org/10.1155/2007/92354
work_keys_str_mv AT jorgeriveranoriega estimatesforthemultiplicativesquarefunctionofsolutionstonondivergenceellipticequations
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