Geodesic
Littlewood--Paley--Rubio de Francia inequality for the Walsh system
Algebra i analiz, Tome 28 (2016) no. 5, pp. 236-246.

Voir la notice de l'article provenant de la source Math-Net.Ru

Rubio de Francia proved the one-sided Littlewood–Paley inequality for arbitrary intervals in $L^p$, $2\le p\infty$. In this article, such an inequality is proved for the Walsh system.
Keywords: Calderón–Zygmund operator, martingales. 
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N. N. Osipov. Littlewood--Paley--Rubio de Francia inequality for the Walsh system. Algebra i analiz, Tome 28 (2016) no. 5, pp. 236-246. http://geodesic.mathdoc.fr/item/AA_2016_28_5_a6/

[1] Rubio de Francia J. L., “A Littlewood–Paley inequality for arbitrary intervals”, Rev. Mat. Iberoamer., 1:2 (1985), 1–14 | DOI | MR | Zbl

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

[3] Kislyakov S. V., Parilov D. V., “O teoreme Litlvuda–Peli dlya proizvolnykh integralov”, Zap. nauch. semin. POMI, 327, 2005, 98–114 | MR | Zbl

[4] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, AFTs, Moskva, 1999

[5] Diestel J., Uhl J. J. (Jr.), Vector measures, Math. Surveys Monogr., 15, Amer. Math. Soc., Providence, RI, 1977 | DOI | MR | Zbl

[6] Gundy R. F., “A decomposition for $L^1$-bounded martingales”, Ann. Math. Statist., 39:1 (1968), 134–138 | DOI | MR | Zbl

[7] Kislyakov S. V., “Martingalnye preobrazovaniya i ravnomerno skhodyaschiesya ortogonalnye ryady”, Zap. nauch. semin. POMI, 141, 1985, 18–38 | MR | Zbl

[8] Stein E. M., Singular integrals and differentiability properties of functions, Princeton Math. Ser., 30, Princeton Univ. Press, Princeton, N.J., 1970 | MR

[9] Burkholder D. L., “Martingale transforms”, Ann. Math. Statist., 37:6 (1966), 1494–1504 | DOI | MR | Zbl