New Gaussian Riesz transforms on variable Lebesgue spaces

We give sufficient conditions on the exponent $p: \mathbb R^d\rightarrow [1,\infty)$ for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue spaces $L^{p(\cdot)}(\mathbb R^d, \gamma_d)$, as well as of the new higher order Riesz transforms associated with the Ornstein-Uhlenbeck semigroup, which are the natural extensions of the supplementary first order Gaussian Riesz transforms defined by A. Nowak and K. Stempak in \cite{nowakstempak}.