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 $J{N}_p$ and the space BMO as well as their vanishing subspaces such as VMO, XMO, CMO, $VJ{N}_p$, and $CJ{N}_p$ 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.

arXiv comment65 pages; Submitted

References in corpus (7)

• Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spaces
• John-Nirenberg lemmas for a doubling measure
• The space $J{N}_p$: nontriviality and duality
• Approximation in Morrey spaces
• Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach
• Aspects of local to global results
• Oscillation estimates, self-improving results and good-$\lambda$ inequalities

Cited by in corpus (3)

• Nontrivial examples of $J{N}_p$ and $VJ{N}_p$ functions
• New John--Nirenberg--Campanato-Type Spaces Related to Both Maximal Functions and Their Commutators
• The John-Nirenberg space: Equality of the vanishing subspaces $VJ{N}_p$ and $CJ{N}_p$