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 9ab8b9d78be339" title="Click to view the MathML source">Lp into 9a191d1f5b61df2383d595453" title="Click to view the MathML source">Lq when and . We show that a ν -order linear fractional integral operator can be continuously extended to a bounded operator from 9ab8b9d78be339" title="Click to view the MathML source">Lp into the Sobolev-BMO space ab6851a303e49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) when 8d572a69a02d03fe733edcb49a579b0"> and 9a849ec7e3d09273afcf06" title="Click to view the MathML source">0≤s<ν satisfy . Likewise, we prove estimates for ν -order bilinear fractional integral operators from ab6" title="Click to view the MathML source">Lp1×Lp2 into ab6851a303e49a0aa16b7b09c57ed" title="Click to view the MathML source">Is(BMO) for various ranges of the indices abde87c643f0155f61d" title="Click to view the MathML source">p1, 9aa63a6786fd8d9bad09b6" title="Click to view the MathML source">p2, and s satisfying .