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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Marcinkiewicz's theorem on operator multipliers of Fourier series


Author: Milutin R. Dostanic
Journal: Proc. Amer. Math. Soc. 132 (2004), 391-396
MSC (2000): Primary 42B15
Published electronically: June 11, 2003
MathSciNet review: 2022361
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Abstract: We give some sufficient conditions on the operators $A_{m}\in\mathcal{B} \left( L^{p}\left( 0,1\right) \right) $ which for each $\Phi_{m}\in L^{p}\left( 0,1\right) $ imply the inequality

\begin{displaymath}\int\limits_{0}^{1}\int\limits_{0}^{2\pi}\left\vert \sum\limi... ..._{m}e^{imx}\cdot \Phi_{m}\left( y\right) \right\vert ^{p}dxdy, \end{displaymath}

$1<p<\infty.$


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Additional Information

Milutin R. Dostanic
Affiliation: Matematicki Fakultet, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia
Email: domi@matf.bg.ac.yu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07017-5
PII: S 0002-9939(03)07017-5
Keywords: Marcinkiewicz's theorem, multipliers
Received by editor(s): July 19, 2001
Received by editor(s) in revised form: September 20, 2002
Published electronically: June 11, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society