Let ${ℬ}_c$ denote the real-valued functions continuous on the extended real line and vanishing at $-\infty$. Let ${ℬ}_r$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\infty$. Define ${𝒜}_c^n$ to be the space of tempered distributions that are the $n$th distributional derivative of a unique function in ${ℬ}_c$. Similarly with ${𝒜}_r^n$ from ${ℬ}_r$. A type of integral is defined on distributions in ${𝒜}_c^n$ and ${𝒜}_r^n$. The multipliers are iterated integrals of functions of bounded variation. For each $n\in \mathbb{N}$, the spaces...