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 Tr. Mat. Inst. Steklova, 2010, Volume 269, Pages 204–214 (Mi tm2897)

Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes

M. K. Potapova, B. V. Simonovb, S. Yu. Tikhonovacd

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Volgograd State Technical University, Volgograd, Russia
c Centre de Recerca Matemàtica, Barcelona, Spain
d Institució Catalana de Recerca i Estudis Avancats, Barcelona, Spain

Abstract: We prove $(L_p,L_q)$ inequalities for mixed moduli of smoothness of positive orders. As corollaries, we obtain embedding theorems for the Nikol'skii classes.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 269, 197–207

Bibliographic databases:

UDC: 517.5
Received in September 2009

Citation: M. K. Potapov, B. V. Simonov, S. Yu. Tikhonov, “Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Tr. Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 204–214; Proc. Steklov Inst. Math., 269 (2010), 197–207

Citation in format AMSBIB
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\paper Relations between mixed moduli of smoothness, and embedding theorems for Nikol'skii classes
\inbook Function theory and differential equations
\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
\serial Tr. Mat. Inst. Steklova
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\vol 269
\pages 204--214
\publ MAIK Nauka/Interperiodica
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Simonov B.V., “Relation between moduli of smoothness and partial sums of Fourier series and embedding theorems for Nikol'skii classes”, Dokl. Math., 83:2 (2011), 265–267
2. M. K. Potapov, B. V. Simonov, “Improvement of the Ul'yanov inequality for mixed moduli of smoothness for functions with lacunary Fourier coefficients”, Moscow University Mathematics Bulletin, 67:1 (2012), 16–22
3. B. V. Simonov, “Mixed Moduli of Smoothness in Mixed Metrics”, Math. Notes, 92:5 (2012), 686–699
4. Lind M., “Estimates of the Total P-Variation of Bivariate Functions”, J. Math. Anal. Appl., 401:1 (2013), 218–231
5. M. K. Potapov, B. V. Simonov, “Properties of mixed moduli of smoothness of functions with lacunary Fourier coefficients”, Moscow University Mathematics Bulletin, 69:1 (2014), 5–15
6. Akgun R., “Mixed modulus of continuity in the Lebesgue spaces with Muckenhouptweights and their properties”, Turk. J. Math., 40:6 (2016), 1169–1192
7. Akgun R., “Mixed Modulus of Smoothness With Muckenhoupt Weights and Approximation By Angle”, Complex Var. Elliptic Equ., 64:2 (2019), 330–351
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