2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214681For the $\bar\partial$-Neumann problem on a regular coordinate domain $Ω\subset \C^{n+1}$, we prove $ε$-subelliptic estimates for an index $ε$ which is in some cases better than $ε=\frac1{2m}$ ($m$ being the {\it multiplicity}) as it was previously proved by Catlin and Cho in \cite{CC08}. This also supplies a much simplified proof of the existing literature. Our approach is founded on the method by Catlin in \cite{C87} which consists in constructing a family of weights $\{ϕ^δ\}$ whose Levi form is bigger than $δ^{-2ε}$ on the $δ$-strip around $\partialΩ$.9 pagesComplex Variables32F10, 32F20, 32N15, 32T25text