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January 2014 $A_{\infty}$ constants between $\mathit{BMO}$ and weighted $\mathit{BMO}$
Yohei Tsutsui
Proc. Japan Acad. Ser. A Math. Sci. 90(1): 11-14 (January 2014). DOI: 10.3792/pjaa.90.11


In this short article, we consider estimates of the ratio \begin{equation*} \|{f}\|_{\mathit{BMO}(w)} / \|{f}\|_{\mathit{BMO}} \end{equation*} from above and below, where $w$ belongs to Muckenhoupt class $A_{\infty}$. The upper bound of the ratio was proved by Hytönen and Pérez in~[6] with the optimal power. We establish the lower bound of the ratio and give two other proofs of the upper bound.


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Yohei Tsutsui. "$A_{\infty}$ constants between $\mathit{BMO}$ and weighted $\mathit{BMO}$." Proc. Japan Acad. Ser. A Math. Sci. 90 (1) 11 - 14, January 2014.


Published: January 2014
First available in Project Euclid: 6 January 2014

zbMATH: 1287.42020
MathSciNet: MR3161539
Digital Object Identifier: 10.3792/pjaa.90.11

Primary: 42B35

Keywords: BMO , Muckenhoupt classes

Rights: Copyright © 2014 The Japan Academy

Vol.90 • No. 1 • January 2014
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