Geodesic
Extension of functions preserving the modulus of continuity
Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 236-245 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of the extension of a real-valued function from a subset of a metric space to the entire space is treated. An extension operator preserving the modulus of continuity of a function is proposed and its properties are studied. An application to the problem of the trace of a locally Lipschitz function on a compact subset of a metric space is given. 
@article{MZM_1997_61_2_a4,
     author = {V. A. Milman},
     title = {Extension of functions preserving the modulus of continuity},
     journal = {Matemati\v{c}eskie zametki},
     pages = {236--245},
     year = {1997},
     volume = {61},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a4/}
}
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V. A. Milman. Extension of functions preserving the modulus of continuity. Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 236-245. http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a4/

[1] Federer G., Geometricheskaya teoriya mery, Nauka, M., 1987 | Zbl

[2] Klyachin A. A., Miklyukov V. M., “Sledy funktsii s prostranstvennopodobnymi grafikami i zadacha o prodolzhenii funktsii pri ogranicheniyakh na gradient”, Matem. sb., 183:7 (1992), 49–64

[3] Mustata C., Extension of Holder functions and some related problems of best approximation, Research Seminars. Preprint No. 7, Babes-Bolyai University. Faculty of Mathematics, 1991, p. 71–86 | MR | Zbl

[4] Timan A. F., Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960

[5] Czipcer J., Cheher L., “Extention of functions satisfying a Lipschitz condition”, Acta Math. Acad. Sci. Hung., 6:1–2 (1955), 213–220 | DOI | MR

[6] Hanin L. G., “Kantorovich–Rubinshtein norm and its application in the theory of Lipschitz spaces”, Proc. Amer. Math. Soc., 115:2 (1992), 345–352 | DOI | MR | Zbl