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Algebra i Analiz, 2010, Volume 22, Issue 2, Pages 164–184 (Mi aa1180)  

This article is cited in 2 scientific papers (total in 2 papers)

Research Papers

Littlewood–Paley inequality for arbitrary rectangles in $\mathbb R^2$ for $0<p\le2$

N. N. Osipov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: The one-sided Littlewood–Paley inequality for pairwise disjoint rectangles in $\mathbb R^2$ is proved for the $L^p$-metric, $0<p\le2$. This result can be treated as an extension of Kislyakov and Parilov's result (they considered the one-dimensional situation) or as an extension of Journé's result (he considered disjoint parallelepipeds in $\mathbb R^n$ but his approach is only suitable for $p\in(1,2]$). We combine Kislyakov and Parilov's methods with methods “dual” to Journé's arguments.

Keywords: Littlewood–Paley inequality, Hardy class, atomic decomposition, Journé lemma, Calderón–Zygmund operator.

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English version:
St. Petersburg Mathematical Journal, 2011, 22:2, 293–306

Bibliographic databases:

Received: 11.09.2009

Citation: N. N. Osipov, “Littlewood–Paley inequality for arbitrary rectangles in $\mathbb R^2$ for $0<p\le2$”, Algebra i Analiz, 22:2 (2010), 164–184; St. Petersburg Math. J., 22:2 (2011), 293–306

Citation in format AMSBIB
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\by N.~N.~Osipov
\paper Littlewood--Paley inequality for arbitrary rectangles in $\mathbb R^2$ for $0<p\le2$
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 2
\pages 164--184
\mathnet{http://mi.mathnet.ru/aa1180}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2668127}
\zmath{https://zbmath.org/?q=an:1219.42011}
\transl
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 2
\pages 293--306
\crossref{https://doi.org/10.1090/S1061-0022-2011-01141-0}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871372089}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. N. Osipov, “One-sided Littlewood–Paley inequality in $\mathbb R^n$ for $0<p\le2$”, J. Math. Sci. (N. Y.), 172:2 (2011), 229–242  mathnet  crossref
    2. N. N. Osipov, “The Littlewood-Paley-Rubio de Francia inequality in Morrey-Campanato spaces”, Sb. Math., 205:7 (2014), 1004–1023  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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