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 ≤ q ≤ p < ∞ and a weight function θ. In the case of q = p = n, θ ≡ 1, 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. © 2018, Pleiades Publishing, Ltd.