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 language | English |
|---|---|
| Pages (from-to) | 1-18 |
| Number of pages | 18 |
| Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
| Volume | 153 |
| Issue number | 1 |
| Early online date | 2021 |
| DOIs | |
| Publication status | Published - 1 Feb 2023 |
| MoE publication type | A1 Journal article-refereed |
Funding
The research was supported by the Academy of Finland.
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
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver