Bla.zej Wr'obel

activity

20222026

collaborators

10 papers

math.CA2026

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

Valentina Ciccone, Błażej Wróbel

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.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

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

Valentina Ciccone, Błażej Wróbel

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.CA2025

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

Maciej Kucharski, Mateusz Kwaśnicki, Błażej Wróbel

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.CA2025

Dimension-free estimates for discrete maximal functions related to normalized sampled gaussians

Mariusz Mirek, Tomasz Z. Szarek, Błażej Wróbel

In this paper, we investigate dimension-free estimates for convolution operators with discrete normalized sampled Gaussians (related to the Theta function) in the context of maxima…

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

Dimension-free Fourier restriction inequalities

Diogo Oliveira e Silva, Błażej Wróbel

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{…

math.FA2024

Dimension-free estimates for low degree functions on the Hamming cube

Komla Domelevo, Polona Durcik, Valentia Fragkiadaki +4

The main result of this paper are dimension-free $L^{p}$ inequalities, $1 < p < \infty$ , for low degree scalar-valued functions on the Hamming cube. More precisely, for any $p > 2,$ $\vare…

math.CA2023

Dimension-free $L^{p}$ estimates for higher order maximal Riesz transforms in terms of the Riesz transforms

Maciej Kucharski, Błażej Wróbel, Jacek Zienkiewicz

We prove a dimension-free $L^{p} (R^{d})$ , $1 < p < \infty$ , estimate for the vector of higher order maximal Riesz transforms in terms of the corresponding Riesz transforms. This i…

math.FA2022

Dimension-free $L^{p}$ estimates for odd order maximal Riesz transforms in terms of the Riesz transforms

Maciej Kucharski, Błażej Wróbel, Jacek Zienkiewicz

We prove a dimension-free $L^{p} (R^{d})$ , $1 < p < \infty$ , estimate for the vector of maximal Riesz transforms of odd order in terms of the corresponding Riesz transforms. This i…

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

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

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

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

Dimension-free estimates for discrete maximal functions related to normalized sampled gaussians

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

Dimension-free Fourier restriction inequalities

Dimension-free estimates for low degree functions on the Hamming cube

Dimension-free Lp estimates for higher order maximal Riesz transforms in terms of the Riesz transforms

Dimension-free Lp estimates for odd order maximal Riesz transforms in terms of the Riesz transforms

Dimension-free $L^{p}$ estimates for higher order maximal Riesz transforms in terms of the Riesz transforms

Dimension-free $L^{p}$ estimates for odd order maximal Riesz transforms in terms of the Riesz transforms