Abstract
Given a homeomorphism ϕ ∈ W 1 M , we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space W 1 F . 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.
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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 4, pp. 834–850, July–August, 2017
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Menovshchikov, A.V. Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space. Sib Math J 58, 649–662 (2017). https://doi.org/10.1134/S0037446617040115
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DOI: https://doi.org/10.1134/S0037446617040115