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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.06964 |
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| _version_ | 1866910112664256512 |
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| author | Vasin, Andrei V. |
| author_facet | Vasin, Andrei V. |
| contents | 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 $\mathcal{S} \subset \mathcal{D}_E$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06964 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Carleson families of cubes related to porous sets Vasin, Andrei V. Functional Analysis 28A75, 28A78 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 $\mathcal{S} \subset \mathcal{D}_E$. |
| title | Carleson families of cubes related to porous sets |
| topic | Functional Analysis 28A75, 28A78 |
| url | https://arxiv.org/abs/2604.06964 |