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 9d78be339" title="Click to view the MathML source">Lp into Lq when 9f221053a0"> and . We show that a ν -order linear fractional integral operator can be continuously extended to a bounded operator from 9d78be339" title="Click to view the MathML source">Lp into the Sobolev-BMO space 9c57ed" title="Click to view the MathML source">Is(BMO) when e733edcb49a579b0"> and b3339a849ec7e3d09273afcf06" title="Click to view the MathML source">0≤s<ν satisfy . Likewise, we prove estimates for ν -order bilinear fractional integral operators from Lp1×Lp2 into 9c57ed" title="Click to view the MathML source">Is(BMO) for various ranges of the indices p1, e79aa63a6786fd8d9bad09b6" title="Click to view the MathML source">p2, and s satisfying .