Disjointification inequalities for Hoeffding subspaces of $H^1$ on an infinite polydisc
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914029875757056 |
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| author | Rzeszut, Maciej |
| author_facet | Rzeszut, Maciej |
| contents | We prove that the $L^1$ norm on the linear span of functions on $\T^\N$ dependent on $m$ variables and analytic and mean zero in each of them can be expressed as an interpolation sum of $H^1\left(\mathbb{T}^S,\ell^1\left(\mathbb{N}^S,H^2\left(\mathbb{T}^{[1,m]\setminus S},\ell^2\left(\mathbb{N}^{[1,m]\setminus S}\right)\right)\right)\right)$ norms over $S\subseteq [1,m]$ and derive some interpolation consequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disjointification inequalities for Hoeffding subspaces of $H^1$ on an infinite polydisc Rzeszut, Maciej Functional Analysis We prove that the $L^1$ norm on the linear span of functions on $\T^\N$ dependent on $m$ variables and analytic and mean zero in each of them can be expressed as an interpolation sum of $H^1\left(\mathbb{T}^S,\ell^1\left(\mathbb{N}^S,H^2\left(\mathbb{T}^{[1,m]\setminus S},\ell^2\left(\mathbb{N}^{[1,m]\setminus S}\right)\right)\right)\right)$ norms over $S\subseteq [1,m]$ and derive some interpolation consequences. |
| title | Disjointification inequalities for Hoeffding subspaces of $H^1$ on an infinite polydisc |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.07624 |