Bla.zej Wr'obel

activity

20242026

collaborators

8 papers

math.CA2026

On high dimensional maximal functions associated to Gaussians, balls, and spheres

Valentina Ciccone, BÅaÅ¼ej WrÃ³bel

We prove that for each $p \in (1, \infty),$ the norms on $L^{p} (R^{d})$ of the maximal functions associated to Gaussians (heat semigroup), balls (Hardy-Littlewood averages), and…

math.CA2026

High-dimensional limits and extremizers for maximal functions associated with log-concave densities

Valentina Ciccone, BÅaÅ¼ej WrÃ³bel

We introduce a unified framework to establish the high-dimensional asymptotic behavior of maximal functions associated with radial log-concave probability densities, encompassing t…

math.CA2026

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

Jakub NiksiÅski, BÅaÅ¼ej WrÃ³bel

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.CA2026

On the dimension-free control of higher order truncated Riesz transforms by higher order Riesz transforms

Maciej Kucharski, Mateusz KwaÅnicki, BÅaÅ¼ej WrÃ³bel

Fix a positive integer $k$ . Let $R_{k}$ be a higher order Riesz transform of order $k$ on $R^{d}$ and let $R_{k}^{t},$ $t > 0,$ be the corresponding truncated Riesz transform. We st…

math.NT2026

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

Dariusz Kosz, Jakub NiksiÅski, BÅaÅ¼ej WrÃ³bel

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 Fourier restriction inequalities

Diogo Oliveira e Silva, BÅaÅ¼ej WrÃ³bel

Let $R_{S^{d - 1}} (p \to q)$ denote the best constant for the $L^{p} (R^{d}) \to L^{q} (S^{d - 1})$ Fourier restriction inequality to the unit sphere $\mathbb{…