We give a characterization of weight functions and on for which the fractional integral operator of order on defined by sends all monotone functions which belong to the weighted Lebesgue space into the weighted Lebesgue space . This characterization is done for all and with and . The analogous Lorentz and Orlicz problems are also considered.
Cite this article
Y. Rakotondratsimba, Weighted Inequalities for the Fractional Integral Operators on Monotone Functions. Z. Anal. Anwend. 15 (1996), no. 1, pp. 75–93DOI 10.4171/ZAA/689