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A projection theorem and tangential boundary behavior of potentials |
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| Authors: | Kohur GowriSankaran David Singman |
| Affiliation: | Department of Mathematics, McGill University, Montreal, Quebec, Canada H3A 2K6 ; Department of Mathematics, George Mason University, Fairfax, Virginia 22030 |
| Abstract: | Let |
| Keywords: | Weinstein equation Littlewood theorem Weinstein potential non-isotropic Hausdorff measure boundary behavior minimal fine limit |
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be the Weinstein operator on the half space, 
. Suppose there is a sequence of Borel sets 
such that a certain tangential projection of 
onto 
forms a pairwise disjoint subset of the boundary. Let 
be a finite test measure on the boundary for a specific non-isotropic Hausdorff measure. The measure 
is carried back to a measure 
on a subset of 
by the projection. We give an upper bound for the Weinstein potential corresponding to the measure 
in terms of a universal constant and a Weinstein subharmonic function. We use this upper bound to deduce a result concerning tangential behavior of Weinstein potentials at the boundary with the exception of sets on the boundary of vanishing non-isotropic Hausdorff measure.