A Survey on Function Spaces of John--Nirenberg Type

TL;DR

This survey reviews recent advances in the study of John--Nirenberg spaces and BMO, including their vanishing subspaces, highlighting key developments and open questions in the field.

Contribution

It provides a comprehensive overview of the latest research on function spaces of John--Nirenberg type and discusses open problems for future exploration.

Findings

Summarizes recent progress on John--Nirenberg spaces and BMO.

Describes properties and relationships of vanishing subspaces.

Presents open questions in the study of these function spaces.

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.