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

Abstract

In this paper we introduce the John-Nirenberg's type spaces ${\text{JN}}_p$ associated with the Gaussian measure $d{\hat{I}}^3(x)=\ddot{I}{€}^{-d/2}{e}^{-|x{|}^2}dx$ in ${\mathbb{R}}^d$ where $1<p<\infty$. We prove a John-Nirenberg inequality for ${\text{JN}}_p({\mathbb{R}}^d,{\hat{I}}^3)$. We also characterize the predual of ${\text{JN}}_p({\mathbb{R}}^d,{\hat{I}}^3)$ as a Hardy type space.

22 pages