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Mat. Zametki, 1995, Volume 58, Issue 2, Pages 218–230 (Mi mz2038)  

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

Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series

B. S. Kashina, S. I. Sharekb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Case Western Reserve University

Abstract: It is proved that for any $N\times N$ orthogonal matrix $A=\{a_{ij}\}$ we have
$$ \sum_{i=1}^N\max_{1\le n\le N}|\sum_{j=1}^na_{ij}| \ge\frac 1{30}N^{1/2}\log N. $$
A multidimensional analog of this result is also established.

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English version:
Mathematical Notes, 1995, 58:2, 824–832

Bibliographic databases:

Received: 27.01.1995

Citation: B. S. Kashin, S. I. Sharek, “Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series”, Mat. Zametki, 58:2 (1995), 218–230; Math. Notes, 58:2 (1995), 824–832

Citation in format AMSBIB
\Bibitem{KasSza95}
\by B.~S.~Kashin, S.~I.~Sharek
\paper Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series
\jour Mat. Zametki
\yr 1995
\vol 58
\issue 2
\pages 218--230
\mathnet{http://mi.mathnet.ru/mz2038}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1367220}
\zmath{https://zbmath.org/?q=an:0857.42019}
\transl
\jour Math. Notes
\yr 1995
\vol 58
\issue 2
\pages 824--832
\crossref{https://doi.org/10.1007/BF02304104}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TV39900019}


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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. B. S. Kashin, “On the possibility of generalizing “correction” theorems”, Math. Notes, 62:6 (1997), 784–786  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. V. Pernai, “Spaces Generated by the Generalized Majorant of Partial Sums”, Math. Notes, 96:1 (2014), 154–157  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математические заметки Mathematical Notes
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