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.
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
\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}