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Dimension-free estimates for semigroup BMO and $A_p$ | | Leonid Slavin
; Pavel Zatitskii
; | | Date: |
7 Aug 2019 | | Abstract: | Let $K_t$ be either the heat or the Poisson kernel on $mathbb{R}^n.$ Let
$mathcal{A}$ stand either for BMO equipped with the quadratic seminorm or for
$A_p,$ $1< pleinfty.$ We establish the following transference between the
class $mathcal{A}$ on an interval $Isubsetmathbb{R}$ and its $K$-version,
$mathcal{A}^K,$ on $mathbb{R}^n$: If a given integral functional admits an
estimate on $mathcal{A}(I),$ then the same estimate holds for
$mathcal{A}^K(mathbb{R}^n),$ with all Lebesgue averages replaced by
$K$-averages. In particular, all such estimates are dimension-free. As an
application, we show that the John--Nirenberg constant of ${
m
BMO}(mathbb{R}^n)$ on balls decays with dimension no faster than $n^{-1/2}.$ | | Source: | arXiv, 1908.2602 | | Services: | Forum | Review | PDF | Favorites | |
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