Sevost’yanov Е. А., Ryazanov Vladimir
(2011)
Equicontinuity of mean quasiconformal mappings.
Siberian Mathematical Journal, 52 (3).
С. 524–536.
Анотація
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 .
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