Boundedness of the Gaussian Riesz Potentials on Gaussian variable Lebesgue spaces

TL;DR

This paper establishes the boundedness of Gaussian Riesz potentials on Gaussian variable Lebesgue spaces, extending known results and providing an alternative proof for classical Gaussian Lebesgue spaces.

Contribution

It proves boundedness of Gaussian Riesz potentials on variable Lebesgue spaces under regularity conditions, extending previous results and offering new insights.

Findings

Boundedness of $I_{\beta}$ on $L^{p(\cdot)}(\gamma_d)$ for $\beta \geq 1$

Extension of boundedness results to variable Lebesgue spaces

Provides an alternative proof for classical Gaussian Lebesgue spaces

Abstract

In this paper we prove the boundedness of the Gaussian Riesz potentials $I_{\beta}$, for $\beta\geq 1$ on $L^{p(\cdot)}(\gamma_d)$, 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 $I_\beta$ on Gaussian Lebesgue spaces $L^p(\gamma_d)$.