English

Extensions of the John-Nirenberg theorem and applications

Classical Analysis and ODEs 2019-10-30 v1

Abstract

The John-Nirenberg theorem states that functions of bounded mean oscillation are exponentially integrable. In this article we give two extensions of this theorem. The first one relates the dyadic maximal function to the sharp maximal function of Fefferman-Stein, while the second one concerns local weighted mean oscillations, generalizing a result of Muckenhoupt and Wheeden. Applications to the context of generalized Poincar\'e type inequalities and to the context of the CpC_p class of weights are given. Extensions to the case of polynomial BMO type spaces are also given.

Keywords

Cite

@article{arxiv.1910.12957,
  title  = {Extensions of the John-Nirenberg theorem and applications},
  author = {Javier Canto and Carlos Pérez},
  journal= {arXiv preprint arXiv:1910.12957},
  year   = {2019}
}