Nemytskii operators between Stepanov almost periodic or almost automorphic function spaces

TL;DR

This paper investigates Nemytskii operators acting between Stepanov almost periodic and almost automorphic function spaces, providing new criteria for their well-definedness and continuity.

Contribution

It establishes necessary and sufficient conditions for Nemytskii operators to be well-defined and continuous between these specialized function spaces.

Findings

Derived new criteria for superposition operators

Characterized conditions for operator continuity

Enhanced understanding of function space mappings

Abstract

We study the superposition operators (also called Nemytskii operators) between spaces of almost periodic (respectively almost automorphic) functions in the sense of Stepanov. We state new results on the superposition, notably we give a necessary and sufficient condition for that these operators are well-defined and continuous.