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A characterization of two-depth Journé packing for bi-parameter and Zygmund rectangles
We completely characterize a two-depth version of Journé's covering lemma in the bi-parameter setting. Let $\mathcal U$ be an incomparable family of bi-parameter dyadic rectangles contained in $Ω$, and write $e_i(I):=e_i(I;Ω)$ for the two embeddedness depths. For every coordinatewise nonincreasing $
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