Geodesic
One-sided Littlewood–Paley inequality in $\mathbb R^n$ for $0$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 88-115 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the one-sided Littlewood–Paley inequality for arbitrary collections of mutually disjoint rectangular parallelepipeds in $\mathbb R^n$ for the $L^p$-metric, $0. The paper supplements the author's earlier work, which dealt with the situation of $n=2$. That work was based on R. Fefferman's theory, which makes it possible to verify the boundedness of certain linear operators on two-parameter Hardy spaces (i.e., Hardy spaces on the product of two Euclidean spaces $H^p(\mathbb R^{d_1}\times\mathbb R^{d_2})$). However, Fefferman's results are not applicable in the situation where the number of Euclidean factors is greater than 2. Here we employ the more complicated Carbery–Seeger theory, which is a further development of Fefferman's ideas. It allows us to verify the boundedness of some singular integral operators on the multiparameter Hardy spaces $H^p(\mathbb R^{d_1}\times\cdots\times\mathbb R^{d_n})$, which leads eventually to the required inequality of Littlewood–Paley type. Bibl. – 13 titles. 
@article{ZNSL_2010_376_a4,
     author = {N. N. Osipov},
     title = {One-sided {Littlewood{\textendash}Paley} inequality in $\mathbb R^n$ for $0<p\le2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {88--115},
     year = {2010},
     volume = {376},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a4/}
}
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N. N. Osipov. One-sided Littlewood–Paley inequality in $\mathbb R^n$ for $0

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