Martín-Reyes, F. J.; de la Torre, A. One-sided BMO spaces. (English) Zbl 0801.42010 J. Lond. Math. Soc., II. Ser. 49, No. 3, 529-542 (1994). In this paper we introduce the one-sided sharp functions defined by \[ f_ +^ \# (x) = \sup_{h > 0} {1 \over h} \int^{x + h}_ x \left( f(y) - {1 \over h} \int^{x + 2h}_{x + h} f \right)^ + dy \] and \[ f_ -^ \# (x) = \sup_{h > 0} {1 \over h} \int^ x_{x - h} \left( f(y) - {1 \over h} \int^{x - h}_{x-2h} f \right)^ + dy \] where \(z^ + = \max (z,0)\). We study the BMO spaces associated to \(f^ \#_ +\) and \(f^ \#_ -\) and their relation with the good weights for the one-sided Hardy-Littlewood maximal functions. Finally, as an application of our results, we characterize the weights for one-sided fractional integrals and one-sided fractional maximal operators. Reviewer: F.J.Martín-Reyes and A.de la Torre (Malaga) Cited in 3 ReviewsCited in 26 Documents MSC: 42B25 Maximal functions, Littlewood-Paley theory 26A33 Fractional derivatives and integrals Keywords:weighted inequalities; bounded mean oscillation; Riemann-Liouville fractional integral operator; BMO spaces; one-sided Hardy-Littlewood maximal functions; one-sided fractional integrals; one-sided fractional maximal operators PDFBibTeX XMLCite \textit{F. J. Martín-Reyes} and \textit{A. de la Torre}, J. Lond. Math. Soc., II. Ser. 49, No. 3, 529--542 (1994; Zbl 0801.42010) Full Text: DOI