On the boundedness of the multilinear fractional integral operators

We derive necessary and sufficient conditions for a weight vv governing the weighted inequality (∫Rn|Iα(f→)(x)|qv(x)dx)1/q≤C∏i=1m(∫Rn|fi(x)|pidx)1/pi, where IαIα is the multilinear fractional integral operator. The derived condition is of D. Adams type and any additional assumption on the weight vv is not assumed.