Dyadic John-Nirenberg space
Functional Analysis
2021-10-11 v2
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.
Keywords
Cite
@article{arxiv.2107.00492,
title = {Dyadic John-Nirenberg space},
author = {Juha Kinnunen and Kim Myyryläinen},
journal= {arXiv preprint arXiv:2107.00492},
year = {2021}
}
Comments
13 pages