We consider m-th order linear, uniformly elliptic equations Lu = f with non-smooth coefficients in Banach-Sobolev spaces W^m/Xw(Ω) generated by weighted Banach Function Spaces Xw(Ω) on a bounded domain Ω ⊂ R^n. Supposing boundedness of the Hardy-Littlewood Maximal operator and the Caldeon-Zygmund singular integrals in Xw(Ω) we obtain  solvability in the small in W^m/Xw(Ω) and establish interior Schauder type a priori estimates.

These results will be used in order to obtain Fredholmness of the operator L in Xw(Ω).