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arXiv · 2604.06964

Carleson families of cubes related to porous sets

Andrei V. Vasin
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Abstract

Given a porous set $E\in \mathbb{R}^d$ and a dyadic lattice $\mathcal{D}$, we refine the Carleson packing condition and the sparseness property for the dyadic cover $\mathcal{D}_E=\{Q \in \mathcal{D}: \: Q \cap E \neq \varnothing\}$. We study the inverse problem, when a Carleson family $\mathcal{S} \subset \mathcal{D}$ generates the porous set $E$ such that $\mathcal{S} \subset \mathcal{D}_E$.

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Andrei V. Vasin. 2026-04-08. Carleson families of cubes related to porous sets. https://arxiv.org/abs/2604.06964

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