Gaussian JNp Spaces

Abstract

In this paper we introduce the John-Nirenberg’s type spaces JNp associated with the Gaussian measure dγ(x) = π−d/2e−|x| 2 dx in Rd where 1 < p < ∞. We prove a John-Nirenberg inequality for JNp(Rd ,γ). We also characterize the predual of JNp(Rd ,γ) as a Hardy type space.