Functions of bounded \(\kappa \varphi\)-variation in the sense of Riesz-Korenblum
Summary: We present the space of functions of bounded \(\kappa \varphi\)-variation in the sense of Riesz-Korenblum, denoted by \(\kappa BV_{\varphi}[a, b]\), which is a combination of the notions of bounded \(\varphi\)-variation in the sense of Riesz and bounded \(\kappa\)-variation in the sense of Korenblum. Moreover, we prove that the space generated by this class of functions is a Banach space with a given norm and we prove that a uniformly bounded composition operator satisfies Matkowski's weak condition.
functions of bounded \(\kappa \varphi\)-variation
scientific article; zbMATH DE number 6167915
scientific article