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arXiv · 1601.03848

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

Leonid Slavin·Vasily Vasyunin
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Abstract

This paper is a continuation of earlier work by the first author who determined the John--Nirenberg constant of ${\rm BMO}^p\big((0,1)\big)$ 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 $1\le p\le 2.$

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Leonid Slavin, Vasily Vasyunin. 2016-01-15. The John--Nirenberg constant of ${\rm BMO}^p$, $p>2$. https://arxiv.org/abs/1601.03848

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