7 papers · 1 filter
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…
On high dimensional maximal functions associated to Gaussians, balls, and spheres
Valentina Ciccone, Błażej Wróbel
We prove that for each the norms on of the maximal functions associated to Gaussians (heat semigroup), balls (Hardy-Littlewood averages), and…
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 . Let be a higher order Riesz transform of order on and let be the corresponding truncated Riesz transform. We st…
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…
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 for $p\in[2,\…
Dimension-free Fourier restriction inequalities
Diogo Oliveira e Silva, Błażej Wróbel
Let denote the best constant for the Fourier restriction inequality to the unit sphere $\mathbb{…
Dimension-free estimates for higher order maximal Riesz transforms in terms of the Riesz transforms
Maciej Kucharski, Błażej Wróbel, Jacek Zienkiewicz
We prove a dimension-free , , estimate for the vector of higher order maximal Riesz transforms in terms of the corresponding Riesz transforms. This i…