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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