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weighted inequalities; Bessel potential operators; Riesz potential operators
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<p\leq q<\infty $.
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