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The Littlewood-Paley-Rubio de Francia inequality in Morrey-Campanato spaces. (English. Russian original) Zbl 1304.42050

Sb. Math. 205, No. 7, 1004-1023 (2014); translation from Mat. Sb. 205, No. 7, 95-114 (2014).
Summary: J. L. Rubio de Francia [Rev. Mat. Iberoam. 1, No. 2, 1–14 (1985; Zbl 0611.42005)] proved a one-sided Littlewood-Paley inequality for arbitrary intervals in \(L^p\), \(2\leq p<\infty\). In this article, his methods are developed and employed to prove an analogue of this type of inequality for exponents \(p\) ‘beyond the index \(p=\infty\)’, that is, for spaces of Hölder functions and \(\mathrm{BMO}\).

MSC:

42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis
46E15 Banach spaces of continuous, differentiable or analytic functions

Citations:

Zbl 0611.42005