  In this paper we study the regularity properties of the Gaussian Bessel
potentials and Gaussian Bessel fractional derivatives on variable Gaussian
Besov-Lipschitz spaces $B_{p(\cdot),q(\cdot)}^{\alpha}(\gamma_{d}),$ that were
defined in a previous paper \cite{Pinrodurb}, under certain conditions on
$p(\cdot)$ and $q(\cdot)$.
