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arXiv · 2208.11864

Boundedness of the Gaussian Riesz Potentials on Gaussian variable Lebesgue spaces

Eduard Navas·Ebner Pineda·Wilfredo O. Urbina
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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 $L^p(\gamma_d)$.

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Eduard Navas, Ebner Pineda, Wilfredo O. Urbina. 2022-08-25. Boundedness of the Gaussian Riesz Potentials on Gaussian variable Lebesgue spaces. https://arxiv.org/abs/2208.11864

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