2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137658This paper gives some simple estimates of the essential norm for the difference of composition operators induced by $ϕ$ and $ψ$ acting on bounded function space in the unit polydiscs $U^n$, where $ϕ(z)$ and $ψ(z)$be holomorphic self-maps of $U^n$. As its applications, a characterization of compact difference is given for composition operators acting on the bounded function spaces.9 pagesFunctional Analysis47B38; 7B38; 26A16; 32A16; 32A26; 32A37text