Geodesic
A two-weight inequality for the Bessel potential operator
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 497-511.

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Necessary conditions and sufficient conditions are derived in order that \linebreak Bessel potential operator $J_{s,\lambda }$ is bounded from the weighted Lebesgue spaces $L_{v}^{p}=L^{p}(\Bbb R^n,v(x)dx)$ into $L_{u}^{q}$ when $1$.
Classification : 26D10, 42B20, 42B25, 46E35, 47B38
Keywords: weighted inequalities; Bessel potential operators; Riesz potential operators 
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     title = {A two-weight inequality for the {Bessel} potential operator},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Rakotondratsimba, Y. A two-weight inequality for the Bessel potential operator. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 497-511. http://geodesic.mathdoc.fr/item/CMUC_1997__38_3_a6/