Characterization of the $\mathrm{RV}_{\phi, 2, \alpha}([a, b])$ space

Abstract

We introduce the $\left(\varphi ,2,\alpha \right)$-bounded variation of a function, a concept that generalizes the $\varphi$-bounded variation introduced by Medvedev. We also provide a characterization to find out the $\left(\varphi ,2,\alpha \right)$-variation of a function $f$ in the sense of Riesz.