Geodesic
Constructive description of Hölder classes on compact subsets of $\mathbb{R}^3$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 48, Tome 491 (2020), pp. 119-144 
D. A. Pavlov. Constructive description of Hölder classes on compact subsets of $\mathbb{R}^3$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 48, Tome 491 (2020), pp. 119-144. http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a6/
@article{ZNSL_2020_491_a6,
     author = {D. A. Pavlov},
     title = {Constructive description of {H\"older} classes on compact subsets of $\mathbb{R}^3$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {119--144},
     year = {2020},
     volume = {491},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We give a constructive description of Hölder classes of functions on a compact subset of a chord-arc curve in $\mathbb{R}^3$ in terms of the rate of approximation by harmonic functions.

[1] V. K. Dzyadyk, “O konstruktivnoi kharakteristike funktsii, udovletvoryayuschikh usloviyu $\text{Lip}~ \alpha$ ( $0\alpha1$) na konechnom otrezke veschestvennoi osi”, Izvestiya AN SSSR, ser. matem., 20:5 (1956), 623–642 | MR

[2] V. V. Andrievskii, “Geometricheskoe stroenie oblastei i pryamye teoremy konstruktivnoi teorii funktsii”, Matem. sb., 126(168):1 (1985), 41–58 | MR

[3] N. A. Shirokov, “Approksimativnaya entropiya kontinuumov”, Dokl. AN SSSR, 235:3 (1977), 546–549 | MR

[4] N. A. Shirokov, “Constructive descriptions of functional classes by polynomial approximations”, J. Math. Sci., 105 (2001), 2269–2291 | DOI | MR

[5] T. A. Alexeeva, N. A. Shirokov, “Constructive description of Hölder-like classes on an arc in $\mathbb{R}^3$ by means of harmonic functions”, J. Approx. Theory, 249 (2020) | DOI | MR | Zbl

[6] E. M. Dyn'kin, “The pseudoanalytic extension”, J. Analyse Mathematique, 60 (1993), 45–70 | DOI | MR | Zbl

[7] V. I. Smirnov, Kurs vysshei matematiki, v. 2, Nauka, M., 1974, 656 pp. | MR