Geodesic
Weighted Calderón–Zygmund decomposition with some applications to interpolation
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 186-200
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Let $X$ be an $\mathrm A_1$-regular lattice of measurable functions and let $Q$ be a projection which is also a Calderón–Zygmund operator. Then it is possible to define a space $X^Q$ consisting of the functions $f\in X$ that satisfy $Qf=f$ in a certain sense. By using the Bourgain approach to interpolation, we establish that the couple $(\mathrm L_1^Q,X^Q)$ is $\mathrm K$-closed in $(\mathrm L_1,X)$. This result is sharp in the sense that, in general, $\mathrm A_1$-regularity cannot be replaced by weaker conditions such as $\mathrm A_p$-regularity for $p>1$. 
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     title = {Weighted {Calder\'on{\textendash}Zygmund} decomposition with some applications to interpolation},
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D. V. Rutsky. Weighted Calderón–Zygmund decomposition with some applications to interpolation. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 186-200. http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a6/

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