The John–Nirenberg Space: Equality of the Vanishing Subspaces VJNp and CJNp

Riikka Korte, Timo Takala*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
33 Downloads (Pure)

Abstract

The John–Nirenberg spaces JNp are generalizations of the space of bounded mean oscillation BMO with JN= BMO . Their vanishing subspaces VJNp and CJNp are defined in similar ways as VMO and CMO, which are subspaces of BMO. As our main result, we prove that VJNp and CJNp coincide by showing that certain Morrey type integrals of JNp functions tend to zero for small and large cubes. We also show that JNp,q(Rn) = Lp(Rn) / R , if p= q .

Original languageEnglish
Article number67
Pages (from-to)1-19
Number of pages19
JournalJOURNAL OF GEOMETRIC ANALYSIS
Volume34
Issue number3
DOIs
Publication statusPublished - Mar 2024
MoE publication typeA1 Journal article-refereed

Keywords

  • Bounded mean oscillation
  • Euclidean space
  • John–Nirenberg inequality
  • John–Nirenberg space
  • Morrey type integral
  • Vanishing subspace

Fingerprint

Dive into the research topics of 'The John–Nirenberg Space: Equality of the Vanishing Subspaces VJNp and CJNp'. Together they form a unique fingerprint.

Cite this