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Zap. Nauchn. Sem. POMI, 2013, Volume 416, Pages 175–187 (Mi znsl5701)  

This article is cited in 2 scientific papers (total in 3 papers)

On the relationship between $\mathrm{AK}$-stability and $\mathrm{BMO}$-regularity

D. V. Rutsky

St. Petersburg Department of Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia

Abstract: 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 $(X, Y)$.

Key words and phrases: $\mathrm{BMO}$-regularity, $\mathrm{AK}$-stability, real interpolation, complex interpolation.

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English version:
Journal of Mathematical Sciences (New York), 2014, 202:4, 601–612

UDC: 517.982.1+517.538
Received: 24.06.2013

Citation: D. V. Rutsky, “On the relationship between $\mathrm{AK}$-stability and $\mathrm{BMO}$-regularity”, Investigations on linear operators and function theory. Part 41, Zap. Nauchn. Sem. POMI, 416, POMI, St. Petersburg, 2013, 175–187; J. Math. Sci. (N. Y.), 202:4 (2014), 601–612

Citation in format AMSBIB
\Bibitem{Rut13}
\by D.~V.~Rutsky
\paper On the relationship between $\mathrm{AK}$-stability and $\mathrm{BMO}$-regularity
\inbook Investigations on linear operators and function theory. Part~41
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 416
\pages 175--187
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5701}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 202
\issue 4
\pages 601--612
\crossref{https://doi.org/10.1007/s10958-014-2065-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84922079226}


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    Erratum

    This publication is cited in the following articles:
    1. D. V. Rutsky, “Weighted Calderón–Zygmund decomposition with some applications to interpolation”, J. Math. Sci. (N. Y.), 209:5 (2015), 783–791  mathnet  crossref  mathscinet
    2. D. V. Rutskii, “Ispravlenie k rabote “O svyazi mezhdu $\mathrm{AK}$-ustoichivostyu i $\mathrm{BMO}$-regulyarnostyu””, Issledovaniya po lineinym operatoram i teorii funktsii. 42, Zap. nauchn. sem. POMI, 424, POMI, SPb., 2014, 201–209  mathnet  mathscinet
    3. D. V. Rutskii, “Veschestvennaya interpolyatsiya prostranstv tipa Khardi: anons i nekotorye zamechaniya”, Issledovaniya po lineinym operatoram i teorii funktsii. 47, Zap. nauchn. sem. POMI, 480, POMI, SPb., 2019, 170–190  mathnet
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