Gaussian $\text{JN}_p$ spaces

TL;DR

This paper introduces Gaussian John-Nirenberg spaces $ ext{JN}_p$ in $ ext{R}^d$, proves a key inequality, and characterizes their predual as a Hardy-type space, advancing harmonic analysis in Gaussian settings.

Contribution

It defines Gaussian $ ext{JN}_p$ spaces, establishes a John-Nirenberg inequality, and characterizes their predual as a Hardy-type space, extending classical analysis to Gaussian measures.

Findings

Proved a John-Nirenberg inequality for Gaussian $ ext{JN}_p$ spaces.

Characterized the predual of $ ext{JN}_p$ as a Hardy-type space.

Extended classical harmonic analysis results to Gaussian measure contexts.

Abstract

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.