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Algebra i Analiz, 2016, Volume 28, Issue 5, Pages 236–246 (Mi aa1511)  
This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

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

N. N. Osipovab

a St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka, 27, 191023, St. Petersburg, Russia
b Norwegian University of Science and Technology (NTNU), IME Faculty, Dep. of Math. Sci., Alfred Getz' vei 1, Trondheim, Norway
Full-text PDF (595 kB) Citations (9)
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Abstract: Rubio de Francia proved the one-sided Littlewood–Paley inequality for arbitrary intervals in Lp, 2⩽p<∞. In this article, such an inequality is proved for the Walsh system.
Keywords: Calderón–Zygmund operator, martingales.
Funding agency Grant number
European Research Consortium for Informatics and Mathematics
National Science Foundation DMS 1265549
Russian Foundation for Basic Research 14-01-31163
14-01-00198
This work was carried out 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 is also supported by RFBR (grant no. 14-01-31163 and no. 14-01-00198).
Received: 10.03.2016
English version:
St. Petersburg Mathematical Journal, 2017, Volume 28, Issue 5, Pages 719–726
DOI: https://doi.org/10.1090/spmj/1469
Bibliographic databases:
Document Type: Article
Language: English
Citation: N. N. Osipov, “Littlewood–Paley–Rubio de Francia inequality for the Walsh system”, Algebra i Analiz, 28:5 (2016), 236–246; St. Petersburg Math. J., 28:5 (2017), 719–726
Citation in format AMSBIB
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\pages 719--726
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Linking options:
  • https://www.mathnet.ru/eng/aa1511
  • https://www.mathnet.ru/eng/aa/v28/i5/p236
    • This publication is cited in the following 9 articles:
    1. Viacheslav Borovitskiy, “Littlewood–Paley–Rubio de Francia inequality for multi‐parameter Vilenkin systems”, Mathematische Nachrichten, 297:3 (2024), 1092  crossref
    2. St. Petersburg Math. J., 35:6 (2024), 1005–1011  mathnet  crossref
    3. V. Borovitskiy, “Littlewood–Paley–Rubio De Francia Inequality for the Two-Parameter Walsh System”, J Math Sci, 261:6 (2022), 746  crossref
    4. Viacheslav Borovitskiy, Nikolay N. Osipov, Anton Tselishchev, “Burkholder meets Gundy: Bellman function method for general operators on martingales”, Advances in Mathematics, 410 (2022), 108746  crossref
    5. A. Tselishchev, “On a Vector-Valued Extension of the Littlewood–Paley–Rubio De Francia Inequality for Walsh Functions”, J Math Sci, 268:6 (2022), 827  crossref
    6. A. S. Tselishchev, “A Littlewood-Paley-Rubio de Francia inequality for bounded Vilenkin systems”, Sb. Math., 212:10 (2021), 1491–1502  mathnet  crossref  crossref  zmath  isi
    7. A. Tselischev, “O vektornoznachnom neravenstve Littlvuda–Peli–Rubio de Fransia dlya sistemy Uolsha”, Issledovaniya po lineinym operatoram i teorii funktsii. 49, Zap. nauchn. sem. POMI, 503, POMI, SPb., 2021, 137–153  mathnet
    8. V. A. Borovitskii, N. N. Osipov, A. S. Tselishchev, “On the Bellman function method for operators on martingales”, Dokl. Math., 103:3 (2021), 118–121  mathnet  crossref  crossref  zmath  elib
    9. V. Borovitskii, “Neravenstvo Litlvuda–Peli–Rubio de Fransia dlya dvuparametricheskoi sistemy Uolsha”, Issledovaniya po lineinym operatoram i teorii funktsii. 48, Zap. nauchn. sem. POMI, 491, POMI, SPb., 2020, 27–42  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
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