An estimate for the measure of the preimage of a ball under $Q_{q,p}$-homeomorphisms

Under study are the homeomorphisms between domains in Euclidean space which belong to a Sobolev class whose geometric properties are governed by controlling the behavior of the capacities of condensers in the preimage through the weighted capacity of the condenser in the image. We obtain some estimates for the measure of the preimage of a ball and inspect the asymptotic behavior at a point.