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Matematicheskie Zametki, 1995, Volume 58, Issue 2, Pages 218–230 (Mi mzm2038)  
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
Full-text PDF (951 kB) Citations (2)
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Abstract: It is proved that for any $N\times N$ orthogonal matrix $A=\{a_{ij}\}$ we have
$$ \sum_{i=1}^N\max_{1\le n\le N}\biggl|\sum_{j=1}^na_{ij}\biggr| \ge\frac 1{30}N^{1/2}\log N. $$
A multidimensional analog of this result is also established.
Received: 27.01.1995
English version:
Mathematical Notes, 1995, Volume 58, Issue 2, Pages 824–832
DOI: https://doi.org/10.1007/BF02304104
Bibliographic databases:
Document Type: Article
Language: Russian
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
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\mathscinet{http://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TV39900019}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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