Nages Shanmugalingam (University of Cincinnati)
Domar's argument and a proof of Carleson estimates
for p-quasiminimizers on John domains in metric
measure spaces
Abstract.
Carleson estimates for harmonic functions on Eulidean domains
is by now well-known. These estimates provide an upper bound for
the decay of harmonic functions near the region of the boundary
where the function decays to zero. Classical techniques use
estimates of capacity density of the complement of the domain
at each such boundary point. This talk will focus on a technique
of Domar useful in proving the Carleson estimates for
$p$-harmonic functions on John domains in certain metric measure
spaces. This talk is based on a joint work with
Prof. Hiroaki Aikawa of Shimane University, Japan.
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