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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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St. Petersburg Mathematical Journal, 2011, 22:2, 293–306
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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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http://mi.mathnet.ru/eng/aa1180 http://mi.mathnet.ru/eng/aa/v22/i2/p164
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This publication is cited in the following articles:
-
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
 -
N. N. Osipov, “The Littlewood-Paley-Rubio de Francia inequality in Morrey-Campanato spaces”, Sb. Math., 205:7 (2014), 1004–1023
 
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