Geodesic
On an estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions
Izvestiya. Mathematics, Tome 26 (1986) no. 2, pp. 347-369 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper establishes best possible conditions, on the degree of approximation of functions $f(x_1,\dots,x_m)$ in $L_p([0,1]^m)$ ($0$) by rational functions, that guarantee that the function $f$ has a $p$th mean differential of order $\lambda>0$ everywhere except on a set of zero Hausdorff ($m-1+\alpha$) measure ($0\alpha\leqslant1$). Bibliography: 11 titles. 
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     title = {On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions},
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E. A. Sevast'yanov. On an estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions. Izvestiya. Mathematics, Tome 26 (1986) no. 2, pp. 347-369. http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a5/

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[4] Sevastyanov E. A., “Skorost ratsionalnoi approksimatsii funktsii i ikh differentsiruemost”, Izv. AN SSSR. Ser. matem., 44:6 (1980), 1410–1416 | MR | Zbl

[5] Sevastyanov E. A., “Ratsionalnaya approksimatsiya i absolyutnaya skhodimost ryadov Fure”, Matem. sb., 107:2 (1978), 227–244 | MR

[6] Karleson L., Izbrannye problemy teorii isklyuchitelnykh mnozhestv, Mir, M., 1971 | MR | Zbl

[7] Sevastyanov E. A., “Kusochno-monotonnaya approksimatsiya i $\Phi$-variatsii”, Anal. Math., 1:2 (1975), 141–164 | DOI | MR

[8] Sevastyanov E. A., “Nekotorye otsenki proizvodnykh ratsionalnykh funktsii v integralnykh metrikakh”, Matem. zametki, 13:4 (1973), 499–510

[9] Gusman M., Differentsirovanie integralov v $\mathbf R^n$, Mir, M., 1978 | MR

[10] Dolzhenko E. P., “Nekotorye metricheskie svoistva algebraicheskikh giperpoverkhnostei”, Izv. AN SSSR. Ser. matem., 27:2 (1963), 241–252

[11] Rusak V. N., “Sopryazhennye ratsionalnye funktsii i otsenki ikh proizvodnykh”, Izv. AN BSSR, seriya fiz.-matem. nauk, 1969, no. 3, 26–33 | MR | Zbl