Geodesic
On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 137-166

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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, characterization by differences, snowflake domain, regular domains, weakly exterior thick domains, thick domains, quasiballs.
Mots-clés : Nikol'skii–Besov spaces, Haar wavelet decomposition, $(\varepsilon,\delta)$-domains 
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     author = {Winfried Sickel},
     title = {On the {Regularity} of {Characteristic} {Functions} of {Weakly} {Exterior} {Thick} {Domains}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {137--166},
     publisher = {mathdoc},
     volume = {323},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2023_323_a7/}
}
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Winfried Sickel. On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 137-166. http://geodesic.mathdoc.fr/item/TM_2023_323_a7/