Jakub Niksiński

activity

20232026

collaborators

6 papers

math.CA2026

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

Mahdi Hormozi, Jakub Niksiński, Błażej Wróbel

We prove that the full discrete Hardy-Littlewood maximal operator associated with Euclidean balls satisfies dimension-free bounds on $ℓ^{p} (Z^{d})$ for every $1 < p < \infty$ . W…

math.CA2026

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

Jakub Niksiński

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 disc…

math.NT2026

Uniform estimates for Delannoy numbers and dimension-free estimates for discrete maximal functions over cross-polytopes

Dariusz Kosz, Jakub Niksiński, Błażej Wróbel

We prove a uniform upper and lower bound for Delannoy numbers. This is achieved by using the representation of Delannoy numbers as the number of lattice points in high-dimensional…

math.CA2025

Dimension-free estimates for discrete maximal functions and lattice points in high-dimensional spheres and balls with small radii

Jakub Niksiński, Błażej Wróbel

We prove that the discrete Hardy-Littlewood maximal function associated with Euclidean spheres with small radii has dimension-free estimates on $ℓ^{p} (Z^{d})$ for $p\in[2,\…

math.CA2024

Remark on dimension-free estimates for discrete maximal functions over $ℓ^{q}$ balls: small dyadic scales

Jakub Niksiński

We give a dimension-free bound on $ℓ^{p} (Z^{d})$ , $p \in [2, \infty]$ for the discrete Hardy-Littlewood maximal operator over the $ℓ^{q}$ balls in $Z^{d}$ with sm…

math.CA2023

Dimension-free estimates on $l^{2} (Z^{d})$ for discrete dyadic maximal function over $l^{1}$ balls: small scales

Jakub Niksiński

We give a dimension-free bound on $l^{p} (Z^{d})$ for discrete Hardy-Littlewood operator over $l^{1}$ balls in $Z^{d}$ with small dyadic radii, where $p \in [2, \infty]$ …

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

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

Uniform estimates for Delannoy numbers and dimension-free estimates for discrete maximal functions over cross-polytopes

Dimension-free estimates for discrete maximal functions and lattice points in high-dimensional spheres and balls with small radii

Remark on dimension-free estimates for discrete maximal functions over ℓq balls: small dyadic scales

Dimension-free estimates on l2(Zd) for discrete dyadic maximal function over l1 balls: small scales

Remark on dimension-free estimates for discrete maximal functions over $ℓ^{q}$ balls: small dyadic scales

Dimension-free estimates on $l^{2} (Z^{d})$ for discrete dyadic maximal function over $l^{1}$ balls: small scales