Osipov, N. N. 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 \(\mathrm{BMO}\). Cited in 1 ReviewCited in 4 Documents MSC: 42B25 Maximal functions, Littlewood-Paley theory 42B35 Function spaces arising in harmonic analysis 46E15 Banach spaces of continuous, differentiable or analytic functions Keywords:Littlewood-Paley-Rubio de Francia inequality; BMO space; Hölder spaces; Lipschitz spaces; Morrey-Campanato spaces Citations:Zbl 0611.42005 × Cite Format Result Cite Review PDF Full Text: DOI arXiv