Boundedness of the Gaussian Riesz Potentials on Gaussian variable Lebesgue spaces

Abstract

In this paper we prove the boundedness of the Gaussian Riesz potentials $I_β$, for $β\geq 1$ on $L^{p(\cdot)}(γ_d)$, the Gaussian variable Lebesgue spaces under a certain additional condition of regularity on $p(\cdot)$ following \cite{DalSco}. Additionally, this result trivially gives us an alternative proof of the boundedness of Gaussian Riesz potentials $I_β$ on Gaussian Lebesgue spaces $L^p(γ_d)$.