Necessary and sufficient condition on weight functions and are derived in order that the Riemann-Liouville fractional integral operator is bounded from the weighted Lebesgue spaces into whenever or . As a consequence for monotone weights then a simple characterization for this boundedness is given whenever . Similar problems for convolution operators, acting on the whole real axis , are also solved.
Cite this article
Y. Rakotondratsimba, Weighted Norm Inequalities for Riemann-Liouville Fractional Integrals of Order Less than One. Z. Anal. Anwend. 16 (1997), no. 4, pp. 801–829DOI 10.4171/ZAA/793