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

Abstract

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

arXiv comment16 pages, 3 figures. To appear in St. Petersburg Math Journal

References in corpus (1)

• The John--Nirenberg constant of ${\mathrm{BMO}}^p,$ $1\le p\le 2$

Cited by in corpus (1)

• Unions of cubes in ${\mathbb{R}}^n$, combinatorics in ${\mathbb{Z}}^n$ and the John-Nirenberg and John-Strömberg inequalities