A Survey on Function Spaces of John--Nirenberg Type

Abstract

In this article, the authors give a survey on the recent developments of both the John--Nirenberg space $JN_p$ and the space BMO as well as their vanishing subspaces such as VMO, XMO, CMO, $VJN_p$, and $CJN_p$ on $\mathbb{R}^n$ or a given cube $Q_0\subset\mathbb{R}^n$ with finite side length. In addition, some related open questions are also presented.