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St. Petersburg Mathematical Journal

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Littlewood-Paley-Rubio de Francia inequality for the Walsh system


Author: N. N. Osipov
Original publication: Algebra i Analiz, tom 28 (2016), nomer 5.
Journal: St. Petersburg Math. J. 28 (2017), 719-726
MSC (2010): Primary 43A75
DOI: https://doi.org/10.1090/spmj/1469
Published electronically: July 25, 2017
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Abstract: Rubio de Francia proved the one-sided Littlewood-Paley inequality for arbitrary intervals in $ L^p$, $ 2\le p<\infty $. In this paper, such an inequality is proved for the Walsh system.


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Additional Information

N. N. Osipov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, 27 Fontanka, 191023 St. Petersburg, Russia; IME Faculty, Department of Mathematical Sciiences, Norwegian University of Science and Technology (NTNU), Alfred Getz’ vei 1, Trondheim, Norway
Email: nicknick@pdmi.ras.ru, nikolai.osipov@math.ntnu.no

DOI: https://doi.org/10.1090/spmj/1469
Keywords: Calder\'on--Zygmund operator, martingales
Published electronically: July 25, 2017
Additional Notes: This paper was written during the tenure of an ERCIM “Alain Bensoussan” Fellowship Programme. During the work on this article, the author made a visit to MSU (Michigan, USA) reimbursed from the grant DMS 1265549. The author was also supported by RFBR (grant nos. 14-01-31163 and 14-01-00198)
Article copyright: © Copyright 2017 American Mathematical Society

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