English

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

R2 v1 2026-06-24T03:48:33.182Z