Mateusz Kwaśnicki

collaborators

8 papers

math.CA2026

Maximal inequalities for derivatives of spherical means

Mateusz KwaÅnicki

We give an alternative formulation of Stein's maximal inequality for generalised spherical averages in terms of derivatives of standard spherical means: if \[ k \ge 0, \qquad d \ge…

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.AP2026

Volumetric density estimates for nonlocal minimal surfaces

Mateusz KwaÅnicki, Jack Thompson

In this article, we prove that viscosity subsolutions to nonlocal mean curvature-type equations satisfy universal volumetric estimates at all scales. Our results hold for general s…

math.AP2025

Poisson kernels on the half-plane are bell-shaped

Mateusz KwaÅnicki

Consider a second-order elliptic operator $L$ in the half-plane $R \times (0, \infty)$ with coefficients depending only on the second coordinate. The Poisson kernel for $L$ …

math.PR2025

Harmonic extension technique: probabilistic and analytic perspectives

Mateusz KwaÅnicki

Consider a path of the reflected Brownian motion in the half-plane ${y \geq 0}$ , and erase its part contained in the interior ${y > 0}$ . What is left is, in an appropriate sense…

math.CA2025

Two-sided bell-shaped sequences

Mateusz KwaÅnicki, Jacek WszoÅa

A nonnegative real function f is bell-shaped if it converges to zero at plus and minus infinity and the nth derivative of f changes sign n times for every n = 0, 1, 2, ... Similarl…