On the Boundedness of Multilinear Fractional Integral Operators

Necessary and sufficient condition governing the boundedness of the multilinear fractional integral operator $T_γ,μ$ defined with respect to a measure μ on a σ-algebra of Borel sets of quasi-metric space X from the product $L_{p}^{1}(X,μ)×⋯×L_{p}^{m}(X,μ)$ to $Lq(X,μ)$ is established. The related weak type inequality is also obtained. The derived results are used to get appropriate boundedness of $T_γ,μ$ in Morrey spaces defined with respect to a measure $μ$.