Regularity of the inverse of a homeomorphism of a Sobolev-Orlicz space

摘要

Given a homeomorphism I center dot a W (M) (1) , we determine the conditions that guarantee the belonging of the inverse of I center dot in some Sobolev-Orlicz space W (F) (1) . We also obtain necessary and sufficient conditions under which a homeomorphism of domains in a Euclidean space induces the bounded composition operator of Sobolev-Orlicz spaces defined by a special class of N-functions. Using these results, we establish requirements on a mapping under which the inverse homeomorphism also induces the bounded composition operator of another pair of Sobolev-Orlicz spaces which is defined by the first pair.