Geodesic
On singular integrals related to the Littlewood–Paley inequality for arbitrary intervals
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 113-119 
S. V. Kislyakov; D. V. Parilov. On singular integrals related to the Littlewood–Paley inequality for arbitrary intervals. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 113-119. http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a6/
@article{ZNSL_2007_345_a6,
     author = {S. V. Kislyakov and D. V. Parilov},
     title = {On singular integrals related to the {Littlewood{\textendash}Paley} inequality for arbitrary intervals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--119},
     year = {2007},
     volume = {345},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The proof of the inequality mentioned in the title requires the knowledge of the fact that operators of a certain class are Calderór–Zygmund singular integral operators. We slightly extend this class.

[1] S. V. Kislyakov, D. V. Parilov, “O teoreme Litlvuda–Peli dlya proizvolnykh intervalov”, Zap. nauchn. semin. POMI, 327, 2005, 98–113

[2] J. L. Rubio de Francia, “A Littlewood–Paley inequality for arbitrary intervals”, Rev. Mat. Iberoamer, 1 (1985), 1–13 | MR

[3] J. Bourgain, “On square functions on the trigonometric system”, Bull. Soc. Math. Belg., 37:1 (1985), 20–26 | MR | Zbl

[4] A. Zigmund, Trigonometricheskie ryady, T. 1, Mir, Moskva, 1965 | MR