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

This article is cited in 7 scientific papers (total in 7 papers)

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
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\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  crossref  mathscinet  zmath  isi  elib  elib  scopus
    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  mathnet  crossref  mathscinet
    3. B. V. Simonov, “Mixed Moduli of Smoothness in Mixed Metrics”, Math. Notes, 92:5 (2012), 686–699  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Lind M., “Estimates of the Total P-Variation of Bivariate Functions”, J. Math. Anal. Appl., 401:1 (2013), 218–231  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathnet  crossref  mathscinet
    6. Akgun R., “Mixed modulus of continuity in the Lebesgue spaces with Muckenhouptweights and their properties”, Turk. J. Math., 40:6 (2016), 1169–1192  crossref  mathscinet  isi  scopus
    7. Akgun R., “Mixed Modulus of Smoothness With Muckenhoupt Weights and Approximation By Angle”, Complex Var. Elliptic Equ., 64:2 (2019), 330–351  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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