Fredholmness of singular integral operators with continuous coefficients on Banach function spaces over the real line

We prove a Fredholm criteria for singular integral operators with continuous coefficients on any separable rearrangement-invariant Banach function space X(R) X ( R ) with nontrivial Boyd indices, and variable Lebesgue spaces with p(· )∈ BM(R) p ( · ) ∈ B M ( R ) .