Abstract
In this paper we show that if the Nemytskii operator maps the \((\phi ,2,\alpha )\)-bounded variation space into itself and satisfies some Lipschitz condition, then there are two functions g and h belonging to the \((\phi ,2,\alpha )\)-bounded variation space such that \(f(t,y)=g(t)y+h(t)\) for all \(t\in [a,b]\), \(y\in {\mathbb {R}}\).
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Castillo, R.E., Rojas, E.M. & Trousselot, E. Nemytskii operator on \((\phi ,2,\alpha )\)-bounded variation space in the sense of Riesz. J. Pseudo-Differ. Oper. Appl. 11, 2023–2043 (2020). https://doi.org/10.1007/s11868-020-00366-8
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DOI: https://doi.org/10.1007/s11868-020-00366-8