Geodesic
Connection between moduli of smoothness in the metrics of $L_p$ and $C$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2015), pp. 8-15 Cet article a éte moissonné depuis la source Math-Net.Ru

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Two inequalities are proved for fractional moduli of smoothness of a function considered in the spaces $L_p$ and $C.$ 
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M. K. Potapov; B. V. Simonov. Connection between moduli of smoothness in the metrics of $L_p$ and $C$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2015), pp. 8-15. http://geodesic.mathdoc.fr/item/VMUMM_2015_1_a1/

[1] Zigmund A., Trigonometricheskie ryady, v. 1, 2, Mir, M., 1965 | MR

[2] Konyushkov A.A., “Nailuchshee priblizhenie trigonometricheskimi polinomami i koeffitsienty Fure”, Matem. sb., 44(86) (1958), 53–86 | MR

[3] Ulyanov P.L., “Vlozhenie nekotorykh klassov funktsii $H_p^{\omega}$”, Izv. AN SSSR. Ser. matem., 32:3 (1968), 649–686 | Zbl

[4] Ulyanov P.L., “Teoremy vlozheniya i sootnosheniya mezhdu nailuchshimi priblizheniyami (modulyami nepreryvnosti) v raznykh metrikakh”, Matem. sb., 81(123):1 (1970), 104–131 | Zbl

[5] Kolyada V.I., “O sootnosheniyakh mezhdu modulyami nepreryvnosti v raznykh metrikakh”, Tr. Matem. in-ta AN SSSR, 181, 1988, 117–136

[6] Potapov M.K., Simonov B.V., Tikhonov S.Yu., “O sootnosheniyakh mezhdu modulyami gladkosti v raznykh metrikakh”, Vestn. Mosk. un-ta. Matem. Mekhan., 2009, no. 3, 17–25 | Zbl

[7] Trebels W., “Inequalities for moduli of smoothness versus embeddings of function spaces”, Arch. Math., 94 (2010), 155–164 | DOI | MR | Zbl

[8] Tikhonov S., Trebels W., “Ul'yanov inequalities and generalized Liouville derivatives”, Proc. Roy. Soc. Edinburgh. Sect. A, 141:1 (2011), 205–224 | DOI | MR | Zbl

[9] Tikhonov S., “Weak type inequalities for moduli of smoothness: the case of limit value parameters”, J. Fourier Anal. Appl., 16:4 (2010), 590–608 | DOI | MR | Zbl

[10] Simonov B., Tikhonov S., “Sharp Ul'yanov-type inequalities using fractional smoothness”, J. Approx. Theory, 162 (2010), 1654–1684 | DOI | MR | Zbl

[11] Potapov M.K., Simonov B.V., Tikhonov S.Yu., “Moduli gladkosti polozhitelnykh poryadkov funktsii iz prostranstv $L_p$, $1 \leq p\leq \infty$”, Matematika. Mekhanika, Sovremennye problemy matematiki i mekhaniki, VII, no. 1, Izd-vo MGU, M., 2011, 100–109

[12] Simonov B.V., Nekotorye voprosy teorii priblizhenii i teoremy vlozheniya, Kand. dis., M., 1985

[13] Bari N.K., Trigonometricheskie ryady, Fiz.-mat. lit., M., 1961 | MR

[14] Nikolskii S.M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

[15] Taberski R., “Differences, moduli and derivatives of fractional orders”, Comment. Math. Prace Mat., 19:2 (1976/77), 389–400 | MR

[16] Khardi G.G., Litlvud D.E., Polia G., Neravenstva, IL, M., 1948