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Mat. Sb. (N.S.), 1978, Volume 106(148), Number 3(7), Pages 380–385 (Mi msb2582)  

This article is cited in 11 scientific papers (total in 11 papers)

Remarks on estimating the Lebesgue functions of an orthonormal system

B. S. Kashin


Abstract: In this paper we clarify the relationship between lower bounds for Lebesgue functions and multiplicative inequalities of Gagliardo–Nirenberg type. We give simple proofs of some theorems on Lebesgue functions.
Bibliography: 10 titles.

Full text: PDF file (464 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1979, 35:1, 57–62

Bibliographic databases:

Document Type: Article
UDC: 517.5
MSC: 42C05, 42C15
Received: 13.02.1978

Citation: B. S. Kashin, “Remarks on estimating the Lebesgue functions of an orthonormal system”, Mat. Sb. (N.S.), 106(148):3(7) (1978), 380–385; Math. USSR-Sb., 35:1 (1979), 57–62

Citation in format AMSBIB
\Bibitem{Kas78}
\by B.~S.~Kashin
\paper Remarks on estimating the Lebesgue functions of an orthonormal system
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 3(7)
\pages 380--385
\mathnet{http://mi.mathnet.ru/msb2582}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=619470}
\zmath{https://zbmath.org/?q=an:0476.42014|0417.42014}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 1
\pages 57--62
\crossref{https://doi.org/10.1070/SM1979v035n01ABEH001450}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17500005}


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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. P. L. Ul'yanov, “Kolmogorov and divergent Fourier series”, Russian Math. Surveys, 38:4 (1983), 57–100  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Shekhtman B., “On Projections in l1 and l-Infinity”, Constr. Approx., 1:4 (1985), 297–303  crossref  mathscinet  zmath  isi
    3. K. S. Kazarian, “Divergent orthogonal Fourier series”, Math. USSR-Sb., 73:2 (1992), 355–377  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Kazaryan K. Ulyanov P., “On the Alexits Problem Concerning Divergence of Orthogonal Fourier-Series”, 316, no. 3, 1991, 542–546  mathscinet  zmath  isi
    5. T. S. Kopaliani, “On a Property of Continuous Operators in $L^p(\mathbb R)$-Space”, Math. Notes, 72:4 (2002), 586–588  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. V. I. Kolyada, “Inequalities of Gagliardo–Nirenberg type and estimates for the moduli of continuity”, Russian Math. Surveys, 60:6 (2005), 1147–1164  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Getsadze R., “The sets of convergence in measure of multiple orthogonal Fourier series”, J. London Math. Soc. (2), 72:1 (2005), 239–257  crossref  mathscinet  zmath  isi  elib
    8. S. V. Bochkarev, “A Generalization of Kolmogorov's Theorem to Biorthogonal Systems”, Proc. Steklov Inst. Math., 260 (2008), 37–49  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. A. I. Parfenov, “Otsenka pogreshnosti obobschennoi formuly M. A. Lavrenteva normoi drobnogo prostranstva Soboleva”, Sib. elektron. matem. izv., 10 (2013), 335–377  mathnet
    10. A. V. Meleshkina, “Fourier Coefficients of Characteristic Functions of Intervals with Respect to a Complete Orthonormal System Bounded in $L^p([0,1])$, $2<p<\infty$”, Math. Notes, 97:4 (2015), 647–651  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. A. V. Meleshkina, “Absolute convergence of Fourier series in bounded complete double orthonormal systems”, Russian Math. Surveys, 71:2 (2016), 379–381  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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