Gaussian $\text{JN}_p$ spaces

In this paper we introduce the John-Nirenberg's type spaces $\text{JN}_p$ associated with the Gaussian measure $d\gamma(x) = \pi^{-d/2}e^{-|x|^2}dx$ in $\mathbb{R}^d$ where $1<p<\infty$. We prove a John-Nirenberg inequality for $\text{JN}_p(\mathbb{R}^d,\gamma)$. We also characterize the predual of $\text{JN}_p(\mathbb{R}^d,\gamma)$ as a Hardy type space.