Littlewood–Paley–Rubio de Francia inequality in Morrey–Campanato spaces: an announcement

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.