Equicontinuity of mean quasiconformal mappings

We establish the equicontinuity and normality of the families RΦ of ring Q(x)-homeomorphisms with integral-type restrictions - Φ(Q(x))dm(x) < ∞ on a domain D ⊂ Rn with n ≥ 2. The resulting conditions on Φ are not only sufficient but also necessary for the equicontinuity and normality
of these families of mappings. We give some applications of these results to the Sobolev classes W1,n loc .