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We consider nonlocal equations of order larger than one with measure data andprove gradient regularity in Sobolev and H\"older spaces as well as pointwisebounds of the gradient in terms of Riesz potentials, leading to fine regularityresults in many commonly used function spaces. The kernel of the integraloperators involves a H\"older dependence in the variables and is not assumed tobe translation invariant.

Gradient regularity and first-order potential estimates for a class of nonlocal equations