Dyadic John-Nirenberg space

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

We discuss the dyadic John-Nirenberg space that is a generalization of functions of bounded mean oscillation. A John-Nirenberg inequality, which gives a weak type estimate for the oscillation of a function, is discussed in the setting of medians instead of integral averages. We show that the dyadic maximal operator is bounded on the dyadic John-Nirenberg space and provide a method to construct nontrivial functions in the dyadic John-Nirenberg space. Moreover, we prove that the John-Nirenberg space is complete. Several open problems are also discussed.

Original languageEnglish
Number of pages18
JournalPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A: MATHEMATICS
DOIs
Publication statusE-pub ahead of print - 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • dyadic
  • John-Nirenberg inequality
  • John-Nirenberg space
  • maximal function
  • median

Fingerprint

Dive into the research topics of 'Dyadic John-Nirenberg space'. Together they form a unique fingerprint.

Cite this