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• W2091720626 abstract "In the study of the local Fatou theorem for harmonic functions, Carleson [Ca] proved the following crucial estimate for positive harmonic functions, now referred to as the Carleson estimate. Given a bounded Lipschitz domain D in the Euclidean space R, there exist constants K,C > 1, depending only on D, with the following property: If ξ ∈ ∂D, if r > 0 is sufficiently small, and if xr is a point in D with |xr − ξ| = r and dist(xr , ∂D) ≥ r/C, then u ≤ Ku(xr) on D ∩ B(ξ, r) whenever u is a positive harmonic function in D ∩ B(ξ,Cr) vanishing continuously on ∂D ∩ B(ξ,Cr). Here B(ξ, r) denotes the open ball with center ξ and radius r. The Carleson estimate has been verified for more general Euclidean domains such as NTA domains, and it plays an important role in the study of harmonic analysis on nonsmooth domains. There are at least three different proofs of the Carleson estimate, based on (i) uniform barriers, (ii) the boundary Harnack principle, and (iii) the mean value inequality of subharmonic functions." @default.
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• W2091720626 date "2005-04-01" @default.
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• W2091720626 title "Carleson type estimates for p-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces" @default.
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• W2091720626 doi "https://doi.org/10.1307/mmj/1114021091" @default.
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