The lower semicontinuity of distortion coefficients of the homeomorphisms inducing bounded composition operators of Sobolev-Orlicz spaces. (English. Russian original) Zbl 1403.46032
Sib. Math. J. 59, No. 2, 332-340 (2018); translation from Sib. Mat. Zh. 59, No. 2, 422-432 (2018).
Summary: We determine the conditions under which the locally uniform limit of mappings generating bounded composition operators of Sobolev-Orlicz spaces also generates an operator of this kind. We estimate the distortion coefficient of the limit mapping.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
Keywords:
Sobolev-Orlicz space; distortion; codistortion; biting convergence; composition operator; \(N\)-functionReferences:
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