Geodesic
Littlewood--Paley--Rubio de Francia inequality in Morrey--Campanato spaces: an announcement
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 117-123

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

A one-sided Littlewood–Paley-type $L^p$-inequality, $2\leq p\infty$, for arbitrary intervals was proved in 1983 by Rubio de Francia. By a refinement of his methods, it is possible to prove an analog of this inequality for “exponents beyond infinity”, i.e., for BMO and Hölder classes. 
@article{ZNSL_2013_416_a6,
     author = {N. N. Osipov},
     title = {Littlewood--Paley--Rubio de {Francia} inequality in {Morrey--Campanato} spaces: an announcement},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {117--123},
     publisher = {mathdoc},
     volume = {416},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a6/}
}
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N. N. Osipov. Littlewood--Paley--Rubio de Francia inequality in Morrey--Campanato spaces: an announcement. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 117-123. http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a6/