In this article, we explore the mapping and boundedness properties of linear and bilinear fractional integral operators acting on Lebesgue spaces with large indices. The prototype ν -order fractional integral operator is the Riesz potential e52e" title="Click to view the MathML source">Iν, and the standard estimates for e52e" title="Click to view the MathML source">Iν are from ae3c94ea2f4c169ab8b9d78be339" title="Click to view the MathML source">Lp into Lq when e6c000b85fd9bd767a409f221053a0"> and becde64ccb">. We show that a ν -order linear fractional integral operator can be continuously extended to a bounded operator from ae3c94ea2f4c169ab8b9d78be339" title="Click to view the MathML source">Lp into the Sobolev-BMO space Is(BMO) when and b3339a849ec7e3d09273afcf06" title="Click to view the MathML source">0≤s<ν satisfy 82b771c8cf17c2eaa6320d3645a2">. Likewise, we prove estimates for ν -order bilinear fractional integral operators from a2ab6" title="Click to view the MathML source">Lp1×Lp2 into Is(BMO) for various ranges of the indices ae8aa964dabde87c643f0155f61d" title="Click to view the MathML source">p1, p2, and s satisfying .