Dariusz Kosz

collaborators

6 papers

math.CA2026

Remarks on the Ionescu-Wainger multiplier theorem

Dariusz Kosz, Mariusz Mirek, Wojciech SÅomian +1

In this paper, we extend the recent Ionescu--Wainger multiplier theorem for the set of canonical fractions by Kosz, Mirek, Peluse, Wan, and Wright in several directions. First, we…

math.NT2026

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

Dariusz Kosz, Jakub NiksiÅski, BÅaÅ¼ej WrÃ³bel

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.DS2026

Polynomial ergodic theorems in the spirit of Dunford and Zygmund

Dariusz Kosz, Bartosz Langowski, Mariusz Mirek +1

The main goal of the paper is to prove convergence in norm and pointwise almost everywhere on $L^{p}$ , $p \in (1, \infty)$ , for certain multiparameter polynomial ergodic averages in th…

math.DS2025

The multilinear circle method and a question of Bergelson

Dariusz Kosz, Mariusz Mirek, Sarah Peluse +2

Let $k \in Z_{+}$ and $(X, B (X), I^¼)$ be a probability space equipped with a family of commuting invertible measure-preserving transformations $T_1,\ldots, T_k \colon…

math.CA2025

Variation of the one-dimensional centered maximal operator on simple functions with gaps between pieces

Paul Hagelstein, Dariusz Kosz, Krzysztof Stempak

Let $M$ denote the centered Hardy--Littlewood operator on $R$ . We prove that \[ {\rm Var} (Mf)\le {\rm Var} (f) - \frac12\big| |f(\infty)|-|f(-\infty)|\big| \] for piecewi…

math.CA2025

On differentiation of integrals in Lebesgue spaces

Marco Fraccaroli, Dariusz Kosz, Luz Roncal

We study the problem of differentiation of integrals for certain bases in the infinite-dimensional torus $T^{I ¨} $ . In particular, for every $p_{0} \in [1, \infty)$ , we construc…