  We consider higher order linear, uniformly elliptic equations with non-smooth
coefficients in Banach-Sobolev spaces generated by weighted general Banach
Function Space (BFS). Supposing boundedness of the Hardy-Littlewood Maximal and
Calderon-Zygmund singular operators in BFSs we obtain local solvability in the
Sobolev-BFS and establish interior Schauder type a priori estimates for the.
elliptic operator. These results will be used in order to obtain Fredholmness
of the operator under consideration in weighted BFSs with suitable weight. In
addition, we analyze some examples of weighted BFS that verify our assumptions
and in which the corresponding Schauder type estimates and Fredholmness of the
operator hold true.
