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

Koskela, Pekka
Nandi, Debanjan

Publication details

All authors or editors: Koskela, Pekka; Nandi, Debanjan; Nicolau, Artur

Journal or series: Proceedings of the American Mathematical Society

ISSN: 0002-9939

eISSN: 1088-6826

Publication year: 2018

Volume: 146

Issue number: 8

Pages range: 3403-3412

Publisher: American Mathematical Society

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1090/proc/13994

Publication open access: Other 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 available: https://arxiv.org/abs/1709.06802

Abstract

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.

Keywords: complex analysis; inequalities (mathematics)

Free keywords: simply connected domains; John domains; Hardy inequality

Fields of science: