Basics of the quasiconformal analysis of a two-index scale of spatial mappings

We define a scale of mappings that depends on two real parameters $p$ and $q$, $n-1\leq q\leq p<\infty$, and a weight function $\theta$ In the case of $q=p=n$, $\theta\equiv1$, we obtain the well-known mappings with bounded distortion. Mappings of a two-index scale inherit many properties of mappings with bounded distortion. They are used for solving a few problems of global analysis and applied problems.