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 8e07cf170075e093857e2fac110ee52e" title="Click to view the MathML source">Iν, and the standard estimates for 8e07cf170075e093857e2fac110ee52e" title="Click to view the MathML source">Iν are from 9d78be339" title="Click to view the MathML source">Lp into Lq when 9e6c000b85fd9bd767a409f221053a0"> and e64ccb">. 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 Is(BMO) when and 9ec7e3d09273afcf06" 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 Is(BMO) for various ranges of the indices p1, p2, and s satisfying 93c118743e88503574a05eb50fa113">.