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Mat. Zametki, 2012, Volume 92, Issue 5, Pages 747–761 (Mi mz9128)  

This article is cited in 2 scientific papers (total in 2 papers)

Mixed Moduli of Smoothness in Mixed Metrics

B. V. Simonov

Volgograd State Technical University

Abstract: For a mixed modulus of smoothness of positive order, its relationship with the norms of partial sums of a Fourier series in a mixed metric is obtained. The relation between mixed moduli of smoothness of positive order in different mixed metrics is established.

Keywords: mixed modulus of smoothness, Fourier series, measurable function, mixed metric, the Weyl derivative, trigonometric polynomial, Hölder's inequality

DOI: https://doi.org/10.4213/mzm9128

Full text: PDF file (519 kB)
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English version:
Mathematical Notes, 2012, 92:5, 686–699

Bibliographic databases:

UDC: 517.5
Received: 03.02.2011

Citation: B. V. Simonov, “Mixed Moduli of Smoothness in Mixed Metrics”, Mat. Zametki, 92:5 (2012), 747–761; Math. Notes, 92:5 (2012), 686–699

Citation in format AMSBIB
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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. 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
    2. M. K. Potapov, B. V. Simonov, “Strengthened Ul'yanov's inequality for complete moduli of smoothness of functions from spaces with mixed metrics”, Moscow University Mathematics Bulletin, 73:6 (2018), 217–228  mathnet  crossref  mathscinet  zmath  isi
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