Geodesic
Inequalities refining relationships between mixed moduli of smoothness in $L_1$- and $L_q$-metrics
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2022), pp. 43-61.

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Some refinements for some relations between mixed moduli of smoothness of fractional orders considered in metrics of $L_1$ and $L_q$ are obtained in the article.
Keywords: inequality, metrics, mixed fractional moduli of smoothness. 
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     author = {M. K. Potapov and B. V. Simonov},
     title = {Inequalities refining relationships between mixed moduli of smoothness in $L_1$- and $L_q$-metrics},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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M. K. Potapov; B. V. Simonov. Inequalities refining relationships between mixed moduli of smoothness in $L_1$- and $L_q$-metrics. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2022), pp. 43-61. http://geodesic.mathdoc.fr/item/IVM_2022_2_a3/

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

[2] Potapov M. K., Simonov B. V., “Otsenki smeshannykh modulei gladkosti v metrikakh $L_q$ cherez smeshannye moduli gladkosti v metrike $L_1$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekhan., 2 (2018), 12–26 | Zbl

[3] Potapov M. K., Simonov B. V., Tikhonov S.Yu., “Analogues of Ulyanov Inequalities for Mixed Moduli of Smoothness”, Methods of Fourier Analysis and Approximation Theory. Appl. and Numerical Harmonic Anal., Birkhauser, Cham, 2016, 161–179 | MR | Zbl

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

[5] Potapov M. K., Simonov B. V., Tikhonov S. Yu., “Sootnosheniya mezhdu smeshannymi modulyami gladkosti i teoremy vlozheniya klassov Nikolskogo”, Tr. MIAN, 269, MAIK, M., 2010, 204–214

[6] Potapov M. K., Simonov B. V., Tikhonov S. Yu., “O sootnosheniyakh mezhdu modulyami gladkosti v raznykh metrikakh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekhan., 3 (2009), 17–25 | Zbl

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

[8] Dominguez O., Tikhonov S., Embedding of smooth function spaces, extrapolations, and related inequalities, 2019, arXiv: 1909.12818v2 [math.FA]

[9] Potapov M. K., Simonov B. V., “Neravenstva razlichnykh metrik dlya trigonometricheskikh polinomov”, Izv. vuzov. Matem., 2019, no. 1, 49–62 | Zbl

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

[11] Potapov M. K., Simonov B. V., “Otsenki chastnykh modulei gladkosti v metrikakh $L_{p_1 \infty}$ i $L_{\infty p_2}$ cherez chastnye moduli gladkosti v metrikakh $L_{p_1 p_2}$”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekhan., 1 (2020), 3–17 | Zbl