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

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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. 
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     author = {S. V. Kislyakov and D. V. Parilov},
     title = {On singular integrals related to the {Littlewood--Paley} inequality for arbitrary intervals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--119},
     publisher = {mathdoc},
     volume = {345},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a6/}
}
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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/