11 papers
Shorter proof of dimension-free estimates for maximal Riesz transforms
Maciej Kucharski, Mateusz Kwaśnicki
We provide a shorter and more direct proof of estimates for maximal Riesz transforms (of an arbitrary order) in terms of the corresponding Riesz transforms, with a constant i…
Maximal inequalities for derivatives of spherical means
Mateusz Kwaśnicki
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…
Volumetric density estimates for nonlocal minimal surfaces
Mateusz Kwaśnicki, 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…
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…
Poisson kernels on the half-plane are bell-shaped
Mateusz Kwaśnicki
Consider a second-order elliptic operator in the half-plane with coefficients depending only on the second coordinate. The Poisson kernel for …
The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis
Serena Dipierro, Mateusz Kwaśnicki, Jack Thompson +1
We revisit a Harnack inequality for antisymmetric functions that has been recently established for the fractional Laplacian and we extend it to more general nonlocal elliptic opera…
Harmonic extension technique: probabilistic and analytic perspectives
Mateusz Kwaśnicki
Consider a path of the reflected Brownian motion in the half-plane , and erase its part contained in the interior . What is left is, in an appropriate sense…
Two-sided bell-shaped sequences
Mateusz Kwaśnicki, Jacek Wszoła
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…
Beurling-Deny formula for Sobolev-Bregman forms
Michał Gutowski, Mateusz Kwaśnicki
For an arbitrary regular Dirichlet form and the associated symmetric Markovian semigroup , we consider the corresponding Sobolev-Bregman form $\mathscr{E}_p(u) =…
Simplicity of eigenvalues of the fractional Laplace operator in an interval
Mateusz Kwaśnicki
We give a short proof of simplicity of the eigenvalues of the fractional Laplace operator in an interval, a result shown recently by Fall, Ghimenti, Micheletti and Pistoia [Calc. V…
Fleming-Viot couples live forever
Mateusz Kwaśnicki
We prove a non-extinction result for Fleming-Viot-type systems of two particles with dynamics described by an arbitrary symmetric Hunt process under the assumption that the referen…