Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations
Keyword(s):
We prove distributional inequalities that imply the comparability of theLpnorms of the multiplicative square function ofuand the nontangential maximal function oflogu, whereuis 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 whenuis a harmonic function is considered.
2016 ◽
Vol 144
(8)
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pp. 3583-3588
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2001 ◽
Vol 64
(1)
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pp. 149-156
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2006 ◽
Vol 136
(6)
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pp. 1131-1155
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