Geodesic
Weighted Estimates for the Riemann--Liouville Operators and Applications
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 289-312

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Necessary and sufficient conditions for the weighted boundedness and compactness of the Riemann–Liouville operators are obtained. Applications to the solvability of the Abel nonlinear integral equations and to the embeddings of Besov-type spaces into weighted Lebesgue spaces on the semiaxis are given. 
@article{TM_2003_243_a19,
     author = {D. V. Prokhorov and V. D. Stepanov},
     title = {Weighted {Estimates} for the {Riemann--Liouville} {Operators} and {Applications}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {289--312},
     publisher = {mathdoc},
     volume = {243},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2003_243_a19/}
}
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D. V. Prokhorov; V. D. Stepanov. Weighted Estimates for the Riemann--Liouville Operators and Applications. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 289-312. http://geodesic.mathdoc.fr/item/TM_2003_243_a19/