Dimension dependence and dimension-free $\ell^2$ estimates for variation seminorms of spherical means on the hypercube
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913142135586816 |
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| author | Łyżwa, Rafał |
| author_facet | Łyżwa, Rafał |
| contents | We prove that the $\ell^2 \to \ell^2$ norm of the $r$-variation seminorm of spherical means on the hypercube admits no dimension-free bounds for any $r \in [1, \infty)$ when the variation is taken over all possible radii. Furthermore, we establish that if the radii are restricted to a fixed parity, dimension-free estimates hold for all $r \in (2, \infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18713 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dimension dependence and dimension-free $\ell^2$ estimates for variation seminorms of spherical means on the hypercube Łyżwa, Rafał Functional Analysis Primary 42C10, Secondary 41A63, 42B15 We prove that the $\ell^2 \to \ell^2$ norm of the $r$-variation seminorm of spherical means on the hypercube admits no dimension-free bounds for any $r \in [1, \infty)$ when the variation is taken over all possible radii. Furthermore, we establish that if the radii are restricted to a fixed parity, dimension-free estimates hold for all $r \in (2, \infty)$. |
| title | Dimension dependence and dimension-free $\ell^2$ estimates for variation seminorms of spherical means on the hypercube |
| topic | Functional Analysis Primary 42C10, Secondary 41A63, 42B15 |
| url | https://arxiv.org/abs/2605.18713 |