On dimension stable spaces of measures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909205997289472 |
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| author | Spector, Daniel Stolyarov, Dmitriy |
| author_facet | Spector, Daniel Stolyarov, Dmitriy |
| contents | In this paper, we define spaces of measures $DS_β(\mathbb{R}^d)$ with dimensional stability $β\in (0,d)$. These spaces bridge between $M_b(\mathbb{R}^d)$, the space of finite Radon measures, and $DS_d(\mathbb{R}^d)= \mathrm{H}^1(\mathbb{R}^d)$, the real Hardy space. We show the spaces $DS_β(\mathbb{R}^d)$ support Sobolev inequalities for $β\in (0,d]$, while for any $β\in [0,d]$ we show that the lower Hausdorff dimension of an element of $DS_β(\mathbb{R}^d)$ is at least $β$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On dimension stable spaces of measures Spector, Daniel Stolyarov, Dmitriy Functional Analysis Analysis of PDEs Classical Analysis and ODEs In this paper, we define spaces of measures $DS_β(\mathbb{R}^d)$ with dimensional stability $β\in (0,d)$. These spaces bridge between $M_b(\mathbb{R}^d)$, the space of finite Radon measures, and $DS_d(\mathbb{R}^d)= \mathrm{H}^1(\mathbb{R}^d)$, the real Hardy space. We show the spaces $DS_β(\mathbb{R}^d)$ support Sobolev inequalities for $β\in (0,d]$, while for any $β\in [0,d]$ we show that the lower Hausdorff dimension of an element of $DS_β(\mathbb{R}^d)$ is at least $β$. |
| title | On dimension stable spaces of measures |
| topic | Functional Analysis Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2405.10728 |