Josephy's theorem, revisited
Daria Bugajewska, Piotr Kasprzak
TL;DR
This paper revisits Josephy's theorem to characterize when composition operators act between spaces of bounded Wiener variation mappings, providing necessary and sufficient conditions for their boundedness.
Contribution
It offers a new characterization of composition operators on Wiener variation spaces, including criteria for local boundedness in a normed-valued context.
Findings
Characterized necessary and sufficient conditions for composition operators.
Established criteria for local boundedness of these operators.
Extended analysis to normed-valued Wiener variation spaces.
Abstract
The main goal of this note is to characterize the necessary and sufficient conditions for a composition operator to act between spaces of mappings of bounded Wiener variation in a normed-valued setting. The necessary and sufficient conditions for local boundedness of such operators are also discussed.
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