English

John-Nirenberg Inequalities and Weight Invariant BMO Spaces

Functional Analysis 2017-07-06 v1

Abstract

This work explores new deep connections between John-Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BMOBMO-type spaces. The results are formulated in a very general framework in which BMOBMO spaces are constructed using a base of sets, used also to define weights with respect to a non-negative measure (not necessarily doubling), and an appropriate oscillation functional. This includes as particular cases many different function spaces on geometric settings of interest. As a consequence the weight invariance of several BMOBMO and Triebel-Lizorkin spaces considered in the literature is proved. Most of the invariance results obtained under this unifying approach are new even in the most classical settings.

Keywords

Cite

@article{arxiv.1707.01141,
  title  = {John-Nirenberg Inequalities and Weight Invariant BMO Spaces},
  author = {Jarod Hart and Rodolfo H. Torres},
  journal= {arXiv preprint arXiv:1707.01141},
  year   = {2017}
}