English

The John--Nirenberg constant of ${\rm BMO}^p$, $p>2$

Classical Analysis and ODEs 2016-01-18 v1

Abstract

This paper is a continuation of earlier work by the first author who determined the John--Nirenberg constant of BMOp((0,1)){\rm BMO}^p\big((0,1)\big) for the range 1p2.1\le p\le 2. Here, we compute that constant for p>2.p>2. As before, the main results rely on Bellman functions for the LpL^p norms of logarithms of AA_\infty weights, but for p>2p>2 these functions turn out to have a significantly more complicated structure than for 1p2.1\le p\le 2.

Keywords

Cite

@article{arxiv.1601.03848,
  title  = {The John--Nirenberg constant of ${\rm BMO}^p$, $p>2$},
  author = {Leonid Slavin and Vasily Vasyunin},
  journal= {arXiv preprint arXiv:1601.03848},
  year   = {2016}
}

Comments

16 pages, 3 figures. To appear in St. Petersburg Math Journal