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Mat. Zametki, 2011, Volume 89, Issue 4, Pages 589–595 (Mi mz9098)  

This article is cited in 6 scientific papers (total in 6 papers)

On an Inequality of Sidon Type for Trigonometric Polynomials

A. O. Radomskii

M. V. Lomonosov Moscow State University

Abstract: We establish a lower bound for the uniform norm of the trigonometric polynomial of special form via the sum of the $L^1$-norms of its summands. This result generalizes a theorem due to Kashin and Temlyakov, which, in turn, generalizes the classical Sidon inequality.

Keywords: trigonometric polynomial, Sidon inequality, lacunary sequence, lacunarity index, Vallée-Poussin kernel

DOI: https://doi.org/10.4213/mzm9098

Full text: PDF file (345 kB)
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English version:
Mathematical Notes, 2011, 89:4, 555–561

Bibliographic databases:

UDC: 517
Received: 17.11.2010

Citation: A. O. Radomskii, “On an Inequality of Sidon Type for Trigonometric Polynomials”, Mat. Zametki, 89:4 (2011), 589–595; Math. Notes, 89:4 (2011), 555–561

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. O. Radomskii, “On the Possibility of Strengthening Sidon-Type Inequalities”, Math. Notes, 94:5 (2013), 829–833  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. P. G. Grigor'ev, A. O. Radomskii, “Some Trigonometric Polynomials with Extremally Small Uniform Norm”, Math. Notes, 98:2 (2015), 230–236  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. O. Radomskii, “On a Sidon-type Inequality for Discrete Orthonormal Systems”, Math. Notes, 101:4 (2017), 693–698  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. O. Radomskii, “On the Sidon inequality for trigonometric polynomials”, St. Petersburg Math. J., 29:4 (2018), 643–656  mathnet  crossref  mathscinet  isi  elib
    5. A. O. Radomskii, “On approximation characteristics of some classes of functions of small smoothness”, Siberian Math. J., 59:3 (2018), 486–493  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. O. Radomskii, “Some properties of the space of quasi-continuous functions”, Russian Math. Surveys, 73:6 (2018), 1119–1121  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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