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Mat. Zametki, 1998, Volume 63, Issue 3, Pages 386–390 (Mi mz1293)  

This article is cited in 1 scientific paper (total in 1 paper)

On a theorem of Marcinkiewicz and Zygmund

S. A. Kirillov

Odessa State Academy of Food Technology

Abstract: Let $\{\varphi_n(x)\}$ be an orthonormal system on the closed interval $[0,1]$, and let $\|\varphi_n\|_\infty\le M_n$. In 1937 Marcinkiewicz and Zygmund obtained an estimate of the norm in $L_q[0,1]$ of the sum of the series $\sum_{n=1}^\infty c_n\varphi_n(x)$ under the condition that $\{M_n\}$ is monotone increasing. In this paper it is shown that this condition cannot be discarded.

DOI: https://doi.org/10.4213/mzm1293

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English version:
Mathematical Notes, 1998, 63:3, 338–341

Bibliographic databases:

UDC: 517.518
Received: 19.04.1996
Revised: 15.10.1997

Citation: S. A. Kirillov, “On a theorem of Marcinkiewicz and Zygmund”, Mat. Zametki, 63:3 (1998), 386–390; Math. Notes, 63:3 (1998), 338–341

Citation in format AMSBIB
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\by S.~A.~Kirillov
\paper On a theorem of Marcinkiewicz and Zygmund
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 3
\pages 386--390
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\crossref{https://doi.org/10.4213/mzm1293}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1631865}
\zmath{https://zbmath.org/?q=an:0922.42018}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 3
\pages 338--341
\crossref{https://doi.org/10.1007/BF02317779}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000075783100008}


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    This publication is cited in the following articles:
    1. T. V. Rodionov, “Analogues of the Hausdorff–Young and Hardy–Littlewood theorems”, Izv. Math., 65:3 (2001), 589–606  mathnet  crossref  crossref  mathscinet  zmath
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