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math.CA2026
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…
math.CA2026
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…
math.AP2026
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 provided their boundary has zer…