Geodesic
Hölder classes in the $L^p$ norm on a chord-arc curve in $\mathbb R^3$
Algebra i analiz, Tome 34 (2022) no. 4, pp. 1-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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On a chord-arc curve $L$ in $\mathbb R^3$, the function class $L_p^{\alpha}\left(L\right)$ is introduced. This class consists of functions that satisfy an $\alpha$-Hölder type condition in the $L^p\left(L\right)$-norm with respect to the arc length on $L$. Our purpose is to describe the functions in $L_p^{\alpha}\left(L\right)$ in terms of the rate of approximation by harmonic functions defined in shrinking neighborhoods of the curve. A statement about possible rate of approximation is proved for a certain subclass of $L_p^{\alpha}\left(L\right)$, a statement ensuring the smootheness of a function approximable with the rate in question is proved for the entire class $L_p^{\alpha}\left(L\right)$.
Keywords: konstructive description, сhord-arc curves.
Mots-clés : Hölder classes harmonic functions 
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T. A. Alekseeva; N. A. Shirokov. Hölder classes in the $L^p$ norm on a chord-arc curve in $\mathbb R^3$. Algebra i analiz, Tome 34 (2022) no. 4, pp. 1-21. http://geodesic.mathdoc.fr/item/AA_2022_34_4_a0/

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