Gaussian ${\text{JN}}_p$ spaces

In this paper we introduce the John-Nirenberg’s type spaces ${\text{JN}}_p$ associated with the Gaussian measure $d\gamma (x)={\pi }^{-d\mathrm{/}2}{e}^{-\mathrm{\mid }x{\mathrm{\mid }}^2}dx$ in ${\mathbb{R}}^d$ where $1<p<\mathrm{\infty }$. 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.