Geodesic
On the boundedness of some classes of integral operators in weighted Lebesgue spaces
Eurasian mathematical journal, Tome 3 (2012) no. 1, pp. 5-17

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Some new Hardy-type inequalities for Hardy-Volterra integral operators are proved and discussed. The case $1$ is considered and the involved kernels satisfy conditions, which are less restrictive than the usual Oinarov condition. 
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     title = {On the boundedness of some classes of integral operators in weighted {Lebesgue} spaces},
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L. S. Arendarenko; R. Oinarov; L.-E. Persson. On the boundedness of some classes of integral operators in weighted Lebesgue spaces. Eurasian mathematical journal, Tome 3 (2012) no. 1, pp. 5-17. http://geodesic.mathdoc.fr/item/EMJ_2012_3_1_a0/