Regularity Theory for Nonlocal Equations with VMO Coefficients

We present a higher regularity result for nonlocal equations with possibly discontinuous coefficients of VMO-type in fractional Sobolev spaces. While for corresponding local elliptic equations with VMO coefficients it is only possible to obtain higher integrability, in our nonlocal setting we are able to also prove a substantial amount of higher differentiability. Therefore, our result is in some sense of purely nonlocal type, following the recent trend of such results in the literature.