Geodesic
Properties of mixed moduli of smoothness of functions with lacunary Fourier coefficients
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2014), pp. 6-17 
M. K. Potapov; B. V. Simonov. Properties of mixed moduli of smoothness of functions with lacunary Fourier coefficients. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2014), pp. 6-17. http://geodesic.mathdoc.fr/item/VMUMM_2014_1_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Certain properties of the mixed moduli of smoothness of functions with lacunary Fourier coefficients are refined in the case of Lebesgue space with a mixed norm.

[1] Potapov M.K., Simonov B.V., Tikhonov S.Yu., “Sootnosheniya mezhdu smeshannymi modulyami gladkosti i teoremy vlozheniya klassov Nikolskogo”, Tr. Matem. in-ta RAN, 269, 2010, 204–214 | Zbl

[2] Simonov B.V., “Vzaimosvyaz modulei gladkosti s chastichnymi summami ryada Fure i teoremy vlozheniya klassov Nikolskogo”, Dokl. RAN, 437:6 (2011), 751–753 | Zbl

[3] Simonov B.V., “Smeshannye moduli gladkosti v smeshannykh metrikakh”, Matem. zametki, 92:5 (2012), 747–761 | DOI | Zbl

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

[5] Potapov M.K., “O priblizhenii “uglom””, Tr. Kollokviuma po konstruktivnoi teorii funktsii (Budapesht, Vengriya, 1969), 371–379

[6] Potapov M.K., Simonov B.V., Tikhonov S.Yu., “Relations for moduli of smoothness in various metrics: functions with restrictions on Fourier coefficients”, Jaen J. Approxim., 1:2 (2009), 205–222 | MR | Zbl

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

[8] Potapov M.K., Simonov B.V., “Utochnenie neravenstva Ulyanova dlya smeshannykh modulei gladkosti funktsii s lakunarnymi koeffitsientami Fure”, Vestn. Mosk. un-ta. Matem. Mekhan., 2012, no. 1, 18–24 | Zbl

[9] Potapov M.K., Simonov B.V., Tikhonov S.Yu., “Mixed moduli of smoothness in $L_p$, $1

\infty$: A survey”, Surv. Approxim. Theory, 8 (2013), 1–57 | MR | Zbl