On multipliers between bounded variation spaces

Abstract

Wiener-type variation spaces, also known as ${BV}_p$-spaces ($1\le p<\infty$), are complete normed linear spaces. A function $g$ is called a multiplier from ${BV}_p$ to ${BV}_q$ if the pointwise multiplication $fg$ belongs to ${BV}_q$ for each $f\in {BV}_p$. In this article, we characterize the multipliers from ${BV}_p$ to ${BV}_q$ for the cases $1\le q<p$ and $1\le p\le q$.