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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Littlewood–Paley–Rubio de Francia inequality for the Walsh system
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by N. N. Osipov
St. Petersburg Math. J. 28 (2017), 719-726
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.
References
  • José L. Rubio de Francia, A Littlewood-Paley inequality for arbitrary intervals, Rev. Mat. Iberoamericana 1 (1985), no. 2, 1–14. MR 850681, DOI 10.4171/RMI/7
  • J. Bourgain, On square functions on the trigonometric system, Bull. Soc. Math. Belg. Sér. B 37 (1985), no. 1, 20–26. MR 847119
  • S. V. Kislyakov and D. V. Parilov, On the Littlewood-Paley theorem for arbitrary intervals, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 327 (2005), no. Issled. po Lineĭn. Oper. i Teor. Funkts. 33, 98–114, 236–237 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 139 (2006), no. 2, 6417–6424. MR 2184431, DOI 10.1007/s10958-006-0359-4
  • B. S. Kashin and A. A. Saakyan, Orthogonal series, Translations of Mathematical Monographs, vol. 75, American Mathematical Society, Providence, RI, 1989. Translated from the Russian by Ralph P. Boas; Translation edited by Ben Silver. MR 1007141, DOI 10.1090/mmono/075
  • J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964
  • Richard F. Gundy, A decomposition for $L^{1}$-bounded martingales, Ann. Math. Statist. 39 (1968), 134–138. MR 221573, DOI 10.1214/aoms/1177698510
  • S. V. Kislyakov, Martingale transformations and uniformly convergent orthogonal series, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 141 (1985), 18–38, 188 (Russian, with English summary). Investigations on linear operators and the theory of functions, XIV. MR 788888
  • Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
  • D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494–1504. MR 208647, DOI 10.1214/aoms/1177699141
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Bibliographic 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
  • 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)
  • © Copyright 2017 American Mathematical Society
  • Journal: St. Petersburg Math. J. 28 (2017), 719-726
  • MSC (2010): Primary 43A75
  • DOI: https://doi.org/10.1090/spmj/1469
  • MathSciNet review: 3637591