An introduction to composition operators in Sobolev spaces
G\'erard Bourdaud
TL;DR
This paper provides an overview of composition operators in Sobolev spaces, focusing on recent results about their continuity, and serves as an introductory survey for researchers in functional analysis.
Contribution
It offers a comprehensive introduction and summarizes recent advances in the study of composition operators in Sobolev spaces.
Findings
Summarizes 2019 results on operator continuity
Highlights key properties of composition operators
Provides foundational knowledge for further research
Abstract
We propose a survey on composition operators in classical Sobolev spaces. We mention results obtained in 2019, on the continuity of such operators.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Holomorphic and Operator Theory · Analytic and geometric function theory