Geodesic
Strengthened Ul'yanov's inequalities for partial moduli of smoothness for functions from spaces with various metrics
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2019), pp. 26-38 
M. K. Potapov; B. V. Simonov. Strengthened Ul'yanov's inequalities for partial moduli of smoothness for functions from spaces with various metrics. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2019), pp. 26-38. http://geodesic.mathdoc.fr/item/VMUMM_2019_3_a3/
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     author = {M. K. Potapov and B. V. Simonov},
     title = {Strengthened {Ul'yanov's} inequalities for partial moduli of smoothness for functions from spaces with various metrics},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {26--38},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_3_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Ul'yanov's inequality connecting moduli of continuity in different metrics is well known for functions of one variable. In this paper functions of two variables are considered. Sharp Ul'yanov's inequalities connecting partial moduli of smoothness of positive order are proved in different mixed metrics.

[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] 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

[3] Potapov M. K., Simonov B. V., Tikhonov S. Yu., “Mixed moduli of smoothness in $L_p$, $1 p \infty$: A Survey”, Surveys in Approximation Theory., 8 (2013), 1–57 | MR | Zbl

[4] Potapov M. K., Simonov B. V., “Polnye moduli gladkosti polozhitelnykh poryadkov funktsii iz prostranstv $L_p$, $1 p \infty$”, Matematika, K 100-letiyu Luzinskogo seminara po teorii funktsii, Sovremennye problemy matematiki i mekhaniki, X, no. 2, Izd-vo Popechitelskogo soveta pri mekh.-mat. f-te MGU im. M.V. Lomonosova, M., 2015, 101–133

[5] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975

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

[7] Potapov M. K., Simonov B. V., “Svoistva chastnogo modulya gladkosti polozhitelnogo poryadka v smeshannoi metrike”, Matematika, Tr. mekh-mat. f-ta MGU imeni M. V. Lomonosova. K 60-letiyu seminara “Trigonometricheskie i ortogonalnye ryady”, Sovremennye problemy matematiki i mekhaniki, X, no. 1, Izd-vo Popechitelskogo soveta pri mekh.-mat. f-te MGU im. M.V. Lomonosova, M., 2014, 58–71

[8] Potapov M. K., Simonov B. V., “Neravenstva raznykh metrik dlya trigonometricheskikh polinomov”, Izv. vuzov. Matematika, 2019, no. 1, 49–62

[9] Uninskii A. P., “Neravenstva v smeshannoi metrike dlya trigonometricheskikh polinomov i tselykh funktsii konechnoi stepeni”, Mat-ly Vsesoyuz. simp. po teoremam vlozheniya (Baku, 1966), 212–213 | MR

[10] Potapov M. K., Simonov B. V., Tikhonov S. Yu., Drobnye moduli gladkosti, MAKS Press, M., 2016