Functional and analytic properties of a class of mappings in quasi-conformal analysis

Abstract

We define a two-index scale , , of homeomorphisms of spatial domains in , the geometric description of which is determined by the control of the behaviour of the -capacity of condensers in the target space in terms of the weighted -capacity of condensers in the source space. We obtain an equivalent functional and analytic description of based on the properties of the composition operator (from weighted Sobolev spaces to non-weighted ones) induced by the inverses of the mappings in . When , the class of mappings coincides with the set of so-called -homeomorphisms which have been studied extensively in the last 25 years.