Geodesic
On the relationship between $\mathrm{AK}$-stability and $\mathrm{BMO}$-regularity
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 175-187 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $(X,Y)$ be a couple of Banach lattices of measurable functions on $\mathbb T\times\Omega$ having the Fatou property and satisfying a certin condition $(*)$ that makes it possible to consistently introduce the Hardy-type subspaces of $X$ and $Y$. We establish that the bounded $\mathrm{AK}$-stability property and the $\mathrm{BMO}$-regularity property are equivalent for such couples. If either lattice $XY'$ is Banach, or both lattices $X^2$ and $Y^2$ are Banach, or $Y=L_p$ with $p\in\{1,2,\infty\}$, then the $\mathrm{AK}$-stability property and the $\mathrm{BMO}$-regularity property are also equivalent for such couples $(X, Y)$. 
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     title = {On the relationship between $\mathrm{AK}$-stability and $\mathrm{BMO}$-regularity},
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D. V. Rutsky. On the relationship between $\mathrm{AK}$-stability and $\mathrm{BMO}$-regularity. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 41, Tome 416 (2013), pp. 175-187. http://geodesic.mathdoc.fr/item/ZNSL_2013_416_a9/

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