擬正則映像與Royden代數

Abstract

Given two arbitary domains G, G' in Rn (n ≧ 3), L.G. Lewis proved that G and G' are quasi-conformally equivalent if and only if their Royden n-algebras are isomorplic. In this article, the analagous results are established for quasi-regular mappings. The author proves that (1) if F:G→G' (G'=F (G) ) is quasiregular, then the Royden n-algebra Mn (G') C 1 (G') can be imbedded into the Royden n-algebra Mn (G) as a subalgebra; and (2) if Royden p-algebras (p≧l) MP (G') and MP (G) are isomorphic, then F is a Qp-mapping. The special case p=n for (2) gives the coverse result of (1).