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arXiv · 2605.18713

Dimension dependence and dimension-free $\ell^2$ estimates for variation seminorms of spherical means on the hypercube

Rafał Łyżwa
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Abstract

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 $r \in (2, \infty)$.

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Rafał Łyżwa. 2026-05-18. Dimension dependence and dimension-free $\ell^2$ estimates for variation seminorms of spherical means on the hypercube. https://arxiv.org/abs/2605.18713

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