2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143644Let $\mathbb{H}$ be the general, reduced Heisenberg group. Our main result establishes the inverse-closedness of a class of integral operators acting on $L^{p}(\mathbb{H})$, given by the off-diagonal decay of the kernel. As a consequence of this result, we show that if $α_{1}I+S_{f}$, where $S_{f}$ is the operator given by convolution with $f$, $f\in L^{1}_{v}(\mathbb{H})$, is invertible in $\B(L^{p}(\mathbb{H}))$, then (α_{1}I+S_{f})^{-1}=α_{2}I+S_{g}$, and $g\in L^{1}_{v}(\mathbb{H})$. We prove analogous results for twisted convolution operators and apply the latter results to a class of Weyl pseudodifferential operators. We briefly discuss relevance to mobile communications.This version corrects two mistakes and recognizes the work of other authors related to a corollary of our main theoremClassical Analysis and ODEs43A20; 47G30text