Properties of functions of generalized bounded variation

Abstract

The class of functions of $\mathrm{\Lambda }B{V}^{(p)}$ shares manyproperties of functions of bounded variation. Here we have shownthat $\mathrm{\Lambda }B{V}^{(p)}$ is a Banach space with a suitable norm,the intersection of $\mathrm{\Lambda }B{V}^{(p)}$, over all sequences$\mathrm{\Lambda }$, is the class of functions of BV${}^{(p)}$ and the unionof $\mathrm{\Lambda }B{V}^{(p)}$, over all sequences $\mathrm{\Lambda }$, is theclass of functions having right- and left-hand limits at every point.