Foundations of Quasiconformal Analysis of a Two-Index Scale of Spatial Mappings

Resumo

A scale of mappings that depends on two real parameters \(p,q\) (\(n - 1 \leqslant q \leqslant p < \infty \)) and a weight function \(\theta \) is defined. In the case \(q = p = n,\)\(\theta \equiv 1,\) well-known mappings with bounded distortion are obtained. The mappings of a two-index scale inherit many properties of mappings with bounded distortion. They are used to solve several problems in global analysis and applied problems.