Geodesic
Refinement of Relations between Mixed Moduli of Smoothness in the Metrics of $L_p$ and $L_\infty$
Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 368-385.

Voir la notice de l'article provenant de la source Math-Net.Ru

Refinements of some relations between mixed moduli of smoothness of fractional orders in the metrics $L_p$ and $L_\infty$ are obtained.
Keywords: inequality, metric, mixed modulus of smoothness of fractional order. 
@article{MZM_2021_110_3_a4,
     author = {M. K. Potapov and B. V. Simonov},
     title = {Refinement of {Relations} between {Mixed} {Moduli} of {Smoothness} in the {Metrics} of $L_p$ and $L_\infty$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {368--385},
     publisher = {mathdoc},
     volume = {110},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a4/}
}
TY  - JOUR
AU  - M. K. Potapov
AU  - B. V. Simonov
TI  - Refinement of Relations between Mixed Moduli of Smoothness in the Metrics of $L_p$ and $L_\infty$
JO  - Matematičeskie zametki
PY  - 2021
SP  - 368
EP  - 385
VL  - 110
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a4/
LA  - ru
ID  - MZM_2021_110_3_a4
ER  - 
%0 Journal Article
%A M. K. Potapov
%A B. V. Simonov
%T Refinement of Relations between Mixed Moduli of Smoothness in the Metrics of $L_p$ and $L_\infty$
%J Matematičeskie zametki
%D 2021
%P 368-385
%V 110
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a4/
%G ru
%F MZM_2021_110_3_a4
M. K. Potapov; B. V. Simonov. Refinement of Relations between Mixed Moduli of Smoothness in the Metrics of $L_p$ and $L_\infty$. Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 368-385. http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a4/

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

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

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

[4] V. I. Kolyada, “O sootnosheniyakh mezhdu modulyami nepreryvnosti v raznykh metrikakh”, Issledovaniya po teorii differentsiruemykh funktsii mnogikh peremennykh i ee prilozheniyam. Chast 12, Tr. MIAN SSSR, 181, Nauka, M., 1988, 117–136 | MR | Zbl

[5] M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “O sootnosheniyakh mezhdu modulyami gladkosti v raznykh metrikakh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2009, no. 3, 17–25 | MR | Zbl

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

[7] S. Tikhonov, “Weak type inequalities for moduli of smoothness: the case of limit value parameters”, J. Fourier Anal. Appl., 16:4 (2011), 590–608 | DOI | MR

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

[9] M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, Drobnye moduli gladkosti, Maks-Press, M., 2016

[10] Yu. Kolomoitsev, S. Tikhonov, Hardy–Littlewood and Ulyanov Inequalities, 2017, arXiv: 1711.08163

[11] M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “Sootnosheniya mezhdu smeshannymi modulyami gladkosti i teoremy vlozheniya klassov Nikolskogo”, Teoriya funktsii i differentsialnye uravneniya, Tr. MIAN, 269, MAIK «Nauka/Interperiodika», M., 2010, 204–214 | MR | Zbl

[12] M. K. Potapov, B. V. Simonov, S. Tikhonov, “Mixed moduli of smoothness in $L_p$, $1 p \infty$: a survey”, Surv. Approx. Theory, 8 (2013), 1–57 | MR

[13] M. K. Potapov, B. V. Simonov, “Svyaz mezhdu smeshannymi modulyami gladkosti v metrikakh $L_p$ i $L_\infty$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2017, no. 3, 21–35 | MR

[14] O. Domingues, S. Tikhonov, Embeddings of Smooth Function Spaces, Extrapolations, and Related Inequalities, 2019, arXiv: 1909.12818

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

[16] A. P. Uninskii, “Neravenstva v smeshannoi norme dlya trigonometricheskikh polinomov i tselykh funktsii konechnoi stepeni”, Materialy Vsesoyuznogo simpoziuma po teoremam vlozheniya, Baku, 1966, 212–218

[17] S. Tikhonov, “Trigonometric series with general monotone coefficients”, J. Math. Anal. Appl., 326:1 (2007), 721–735 | DOI | MR

[18] S. Tikhonov, “Trigonometric series of Nikol'skii classes”, Acta Math. Hungar., 114:1-2 (2007), 61–78 | DOI | MR