In Rn, we prove Lp1 ×· · ·×LpK boundedness for the multilinear fractional integrals Iα(f1, . . . , fK)(x) = R f1(x− θ1y) . . . fK(x− θKy)|y|α−n dy where the θj ’s are nonzero and distinct. We also prove multilinear versions of two inequalities about fractional integrals and a multilinear Lebesgue differentiation theorem.
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