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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 323, Pages 137–166
DOI: https://doi.org/10.4213/tm4363
(Mi tm4363)
 

On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains

Winfried Sickel

Friedrich Schiller University Jena, 07737 Jena, Germany
References:
Abstract: Let $E$ be a domain in $\mathbb R^d$. We investigate the regularity of the characteristic function $\mathcal X_E$ depending on the behavior of the $\delta $-neighborhoods of the boundary of $E$. The regularity is measured in terms of the Nikol'skii–Besov and Lizorkin–Triebel spaces.
Keywords: Lizorkin–Triebel spaces, Nikol'skii–Besov spaces, characterization by differences, Haar wavelet decomposition, snowflake domain, regular domains, weakly exterior thick domains, thick domains, $(\varepsilon,\delta)$-domains, quasiballs.
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Received: December 23, 2022
Revised: July 10, 2023
Accepted: August 1, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 323, Pages 130–158
DOI: https://doi.org/10.1134/S0081543823050085
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: Winfried Sickel, “On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains”, Theory of Functions of Several Real Variables and Its Applications, Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday, Trudy Mat. Inst. Steklova, 323, Steklov Mathematical Institute of RAS, Moscow, 2023, 137–166; Proc. Steklov Inst. Math., 323 (2023), 130–158
Citation in format AMSBIB
\Bibitem{Sic23}
\by Winfried~Sickel
\paper On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains
\inbook Theory of Functions of Several Real Variables and Its Applications
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 323
\pages 137--166
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4363}
\crossref{https://doi.org/10.4213/tm4363}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 323
\pages 130--158
\crossref{https://doi.org/10.1134/S0081543823050085}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85186926565}
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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