We will discuss a possible approach to establish elliptic estimates for operators with barely continuous coefficients in a Sobolev-Besov and Triebel-Lizorkin scale. It is based on certain scaling properties of functions in the aforementioned scales. The problem is slightly nonlinear, and we use the Littlewood-Paley theory to establish the scaling properties. The results are mostly not new but the proposed approach is relatively elementary and therefore of interest.