Geometric theory of composition operators on Sobolev spaces

Vladimir Gol’dshtein; Alexander Ukhlov

doi:10.1007/s10958-025-07745-w

Geometric theory of composition operators on Sobolev spaces

Vladimir Gol’dshtein, Alexander Ukhlov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we present the basic concepts of the geometric theory of composition operators on Sobolev spaces. The main objects of the theory are topological mappings which generate bounded embedding operators on Sobolev spaces by the composition rule. This theory is in some sense a “generalization” of the theory of quasiconformal mappings, but the theory of composition operators is oriented to its applications to the Sobolev embedding theorems, the spectral theory of elliptic operators and continuum mechanics problems.

Original language	English
Pages (from-to)	556-589
Number of pages	34
Journal	Journal of Mathematical Sciences (United States)
Volume	288
Issue number	5
DOIs	https://doi.org/10.1007/s10958-025-07745-w
State	Published - 1 Mar 2025

Keywords

Composition operators
Sobolev spaces

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-025-07745-w

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Geometric theory of composition operators on Sobolev spaces

Abstract

Keywords

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