Abstract:Necessary conditions and sufficient conditions are derived in order that 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 $.
Keywords: weighted inequalities, Bessel potential operators, Riesz potential operators
AMS Subject Classification: Primary 42B25