Accessible parts of boundary for simply connected domains

Pekka Koskela, Debanjan Nandi, Artur Nicolau

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Resum

© 2018 American Mathematical Society. For a bounded simply connected domain Ω ⊂ R2, any point z ∈ Ω and any 0 < α < 1, we give a lower bound for the α-dimensional Hausdorff content of the set of points in the boundary of Ω which can be joined to z by a John curve with a suitable John constant depending only on α, in terms of the distance of z to ∂Ω. In fact this set in the boundary contains the intersection ∂Ωz ∩∂Ω of the boundary of a John subdomain Ωz of Ω, centered at z, with the boundary of Ω. This may be understood as a quantitative version of a result of Makarov. This estimate is then applied to obtain the pointwise version of a weighted Hardy inequality.
Idioma originalAnglès
Pàgines (de-a)3403-3412
RevistaProceedings of the American Mathematical Society
Volum146
Número8
DOIs
Estat de la publicacióPublicada - 1 de gen. 2018

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