Geodesic
Interrelations between full moduli of smoothness in the metrics of $L_1$ и $L_\infty$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 16-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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Interrelation between full moduli of smoothness of natural orders in the metrics $L_1$ and $L_\infty$ is considered in the paper. 
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M. K. Potapov; B. V. Simonov. Interrelations between full moduli of smoothness in the metrics of $L_1$ и $L_\infty$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 16-24. http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a2/

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

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

[3] Potapov M.K., Simonov B.V., Tikhonov S.Yu., “Ob odnom neravenstve P. L. Ulyanova”, Vestn. Mosk. un-ta. Matem. Mekhan., 2008, no. 3, 33–35 | MR

[4] Potapov M., Simonov B., Tikhonov S., “Mixed moduli of smoothness in $L_p$, $1 p \infty.$ A survey”, Surveys Approx. Theory, 8 (2013), 1–57 | MR | Zbl

[5] Potapov M.K., Simonov B.V., Tikhonov S.Yu., “Moduli gladkosti drobnykh poryadkov funktsii iz prostranstv $L_p$, $1 p \infty$”, Matematika, Sovremennye problemy matematiki i mekhaniki: Tr. mekh.-mat. f-ta MGU, VI, no. 1, Izd-vo MGU, M., 2011, 90–110

[6] Potapov M.K., Simonov B.V., “Analogi neravenstva Ulyanova dlya drobnykh modulei gladkosti”, Matematika, Sovremennye problemy matematiki i mekhaniki: Tr. mekh.-mat. f-ta MGU, VIII, no. 1, Izd-vo MGU, M., 2013, 62–70

[7] Potapov M.K., Simonov B.V., “Svyaz mezhdu modulyami gladkosti v metrikakh $L_p$ i $C$”, Vestn. Mosk. un-ta. Matem. Mekhan., 2015, no. 1, 7–16

[8] Potapov M.K., Simonov B.V., “Moduli gladkosti polozhitelnykh poryadkov funktsii prostranstv $L_p$, $1 \leq p \leq \infty$”, Matematika. Mekhanika, Sovremennye problemy matematiki i mekhaniki: Tr. mekh.-mat. f-ta MGU, VII, no. 1, Izd-vo MGU, M., 2011, 100–104

[9] Kolyada V.I., “O sootnosheniyakh mezhdu modulyami nepreryvnosti v raznykh metrikakh”, Tr. Matem. in-ta AN SSSR, 181, 1988, 117–135

[10] Ditzian Z., Tikhonov S., “Ul'yanov and Nikol'skii-type inequalities”, J. Approx. Theory, 133 (2005), 100–133 | DOI | MR | Zbl

[11] Simonov B., Tikhonov S., “Sharp Ul'yanov-type inequalities using fractional smoothness”, J. Approx. Theory, 162:9 (2010), 1654–1684 | DOI | MR | Zbl

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

[13] Potapov M.K., Simonov B.V., Tikhonov S.Yu., “Constructive characteristics of mixed moduli of smoothness of positive orders”, Proc. 8th Congress Int. Society for Analysis, its Applications, and Computation (August 22–27, 2011), v. 2, People's Friendship University of Russia, M., 2012, 314–325 | MR | Zbl

[14] Simonov B.V., Tikhonov S.Yu., “Teoremy vlozheniya v konstruktivnoi teorii priblizhenii”, Matem. sb., 199:9 (2008), 107–148 | DOI | MR | Zbl

[15] Potapov M.K., “O priblizhenii uglom”, Tr. konf. po konstruktivnoi teorii funktsii, Izd-vo AN Vengrii, Budapesht, 1971, 371–399

[16] Potapov M.K., Simonov B.V., “Svoistva chastnogo modulya gladkosti polozhitelnogo poryadka v smeshannoi metrike”, Matematika, Sovremennye problemy matematiki i mekhaniki: Tr. mekh.-mat. f-ta MGU, Kh, no. 1, Izd-vo Popechitelskogo Soveta mekh.-mat. f-ta MGU im. M.V. Lomonosova, M., 2014, 58–70 | MR

[17] Potapov M.K., Simonov B.V., Tikhonov S.Yu., Moduli gladkosti drobnykh poryadkov, v. II, Izd-vo Popechitelskogo Soveta mekh.-mat. f-ta MGU im. M.V. Lomonosova, M., 2015, 1–104

[18] Timan M.F., “O vlozhenii $L_p^{(k)}$ klassov funktsii”, Izv. vuzov, 149:10 (1974), 61–74 | MR | Zbl

[19] Taberski R., “Differences, moduli and derivatives of fractional orders”, Roczn. Comment. Math. Prace Mat. 1976/1977, 19:2, 389–400 | MR | Zbl

[20] Potapov M.K., Simonov B.V., Tikhonov S.Yu., Moduli gladkosti drobnykh poryadkov, Izd-vo Popechitelskogo Soveta mekh.-mat. f-ta MGU im. M.V. Lomonosova, M., 2014, 1–136

[21] Timan M.F., “O raznostnykh svoistvakh funktsii mnogikh peremennykh”, Izv. AN SSSR. Cer. matem., 33 (1967), 667–676