Geodesic
Two-Weight Inequalities for Integral Operators in $L_p$-Spaces of Banach-Valued Functions and Their Applications
Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 194-212

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In the spaces $L_p(\Omega _k;B)$, strong- and weak-type two-weight inequalities are obtained for integral operators arising from the Il'in–Besov integral representation in the case of radial weights. 
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     author = {V. S. Guliev and R. A. Bandaliev},
     title = {Two-Weight {Inequalities} for {Integral} {Operators} in $L_p${-Spaces} of {Banach-Valued} {Functions} and {Their} {Applications}},
     journal = {Informatics and Automation},
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     volume = {243},
     year = {2003},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a13/}
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V. S. Guliev; R. A. Bandaliev. Two-Weight Inequalities for Integral Operators in $L_p$-Spaces of Banach-Valued Functions and Their Applications. Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 194-212. http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a13/