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Some remarks on local operators in generalized Hölder function spaces

Wróbel Małgorzata

Journal of Applied Mathematics and Computational Mechanics

2025

Vol. 24, nr 1

78--88

We discuss the form of local operators, sometimes called operators with memory, acting between spaces of generalized Hölder functions defined on the compact metric spaces and taking values in the special norm spaces. Using the McShane and the Minty extension theorems, we show that in some cases the operators of such a type become Nemytskij composition operators. Moreover, the uniformly bounded as well as the uniformly continuous local operators acting between different Holder function spaces are investigated.