A1 Journal article (refereed)
Accessible parts of boundary for simply connected domains (2018)

Koskela, P., Nandi, D., & Nicolau, A. (2018). Accessible parts of boundary for simply connected domains. Proceedings of the American Mathematical Society, 146(8), 3403-3412. https://doi.org/10.1090/proc/13994

JYU authors or editors

Publication details

All authors or editorsKoskela, Pekka; Nandi, Debanjan; Nicolau, Artur

Journal or seriesProceedings of the American Mathematical Society



Publication year2018


Issue number8

Pages range3403-3412

PublisherAmerican Mathematical Society

Publication countryUnited States

Publication languageEnglish


Publication open accessOther way freely accessible online

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/59827

Web address where publication is availablehttps://arxiv.org/abs/1709.06802


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.

Keywordscomplex analysisinequalities (mathematics)

Free keywordssimply connected domains; John domains; Hardy inequality

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Ministry reportingYes

Reporting Year2018

JUFO rating2

Last updated on 2024-11-05 at 18:05