Accessible parts of boundary for simply connected domains
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
Published inProceedings of the American Mathematical Society
© 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.
PublisherAmerican Mathematical Society
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland
Funding program(s)Centre of Excellence, AoF
Additional information about fundingThe third author was partially supported by the grants 2014SGR75 of Generalitat de Catalunya and MTM2014-51824-P and MTM2017-85666-P of Ministerio de Ciencia e Innovación. The first and second authors were partially supported by the Academy of Finland grant 307333.
Showing items with similar title or keywords.
Iwaniec, Tadeusz; Onninen, Jani (American Mathematical Society, 2019)A remarkable result known as Rad´o-Kneser-Choquet theorem asserts that the harmonic extension of a homeomorphism of the boundary of a Jordan domain ⌦ ⇢ R2 onto the boundary of a convex domain Q ⇢ R2 takes ⌦ di↵eomorphically ...
Lehrbäck, Juha (University of Jyväskylä, 2008)
Neittaanmäki, Pekka; Sokolowski, J.; Zolesio, J. P. (University of Jyväskylä, 1986)
Zhu, Zheng (Finnish Mathematical Society, 2022)Olkoon Ω⊂Rn−1 rajoitettu tähtimäinen alue ja Ωψ ulkoneva kärkialue, jonka kanta-alue on Ω. Arvoilla 1< p≤ ∞ osoitamme, että W1,p(Ωψ) = M1,p(Ωψ) jos ja vain jos W1,p(Ω) = M1,p(Ω).
Kurki, Emma-Karoliina; Vähäkangas, Antti V. (Springer, 2021)We prove a local two-weight Poincaré inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman–Stein inequality for the ...