Author

Jakub Niksiński

2 papers indexed here

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Preprint Aug 2026

High-dimensional discrete 1-symmetric convex bodies and dimension-free estimates for maximal functions

We investigate the behavior of lattice points in 1-symmetric convex bodies--those invariant under both coordinate permutations and sign changes. In this setting we introduce a discrete analogue of the isotropic constant and establish concentration of mass properties for lattice points that parallel classical mass conce...

Jakub Niksiński · 4 citations · ⚡1

Preprint Sep 2026

Dimension-free estimates for full discrete maximal functions associated with Euclidean balls and spheres

We prove that the full discrete Hardy-Littlewood maximal operator associated with Euclidean balls satisfies dimension-free bounds on $\ell^p(\mathbb Z^d)$ for every $1<p<\infty$. We also establish analogous dimension-free bounds for the full discrete spherical maximal operator when $d\geq 5$ and $2\leq p<\infty$. The m...

M. Hormozi, Jakub Niksiński, Bla.zej Wr'obel · 1 citation · ⚡1