Dariusz Kosz

activity

20172026

most citedOn relations between weak and restricted weak type inequalities for maximal operators on non-doubling metric measure spaces

4 citations · 8 across the 20 of their papers we have counts for

collaborators

24 papers

math.CA2026

Remarks on the Ionescu-Wainger multiplier theorem

Dariusz Kosz, Mariusz Mirek, Wojciech Słomian +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 Niksiński, Błażej Wróbel

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.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 $T^{ω}$ . In particular, for every $p_{0} \in [1, \infty)$ , we construct…

math.DS2024

The multilinear circle method and a question of Bergelson

Dariusz Kosz, Mariusz Mirek, Sarah Peluse +2

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

math.CA2024

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.DS2023★ 2 cited

Sharp constants in inequalities admitting the Calderón transference principle

Dariusz Kosz

The aim of this note is twofold. Firstly, we prove an abstract version of the Calderón transference principle for inequalities of admissible type in the general commutative multili…

math.DS2023

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.CA2022

Weak-type maximal function estimates on the infinite-dimensional torus

Dariusz Kosz, Guillermo Rey, Luz Roncal

We prove necessary and sufficient conditions for the weak- $L^{p}$ boundedness, for $p \in (1, \infty)$ , of a maximal operator on the infinite-dimensional torus. In the endpoint case $…

math.CA2022

On the doubling condition in the infinite-dimensional setting

Dariusz Kosz

We present a systematic approach to the problem whether a topologically infinite-dimensional space can be made homogeneous in the Coifman--Weiss sense. The answer to the examined q…

math.CA2022

Sharp estimates for Jacobi heat kernels in conic domains

Dawid Hanrahan, Dariusz Kosz

We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone $V^{d + 1}$ and its surface $V_{0}^{d + 1}$ . To do…

math.CA2022

The maximal function of the Devil's staircase is absolutely continuous

Cristian González-Riquelme, Dariusz Kosz

We study the problem of whether the centered Hardy--Littlewood maximal function of a singular function is absolutely continuous. For a parameter $d \in (0, 1)$ and a closed set $E\s…

math.CA2021

Maximal operators in nondoubling metric measure spaces

Dariusz Kosz

This is a revised version of the doctoral dissertation of the same title, written under the supervision of Professor Krzysztof Stempak in 2019. For general (possibly nondoubling) m…

math.CA2021

Maximal operators on the infinite-dimensional torus

Dariusz Kosz, Javier Martínez Perales, Victoria Paternostro +2

We study maximal operators related to bases on the infinite-dimensional torus $T^{ω}$ . {For the normalized Haar measure $d x$ on $T^{ω}$ it is known that $M^{\mathcal{…

math.CA2021

$A_{\infty}$ condition for general bases revisited: complete classification of definitions

Dariusz Kosz

We refer to the discussion on different characterizations of the $A_{\infty}$ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi. Twelve definitions of the $A_\…

math.CA2020★ 1 cited

Some remarks on dimension-free estimates for the discrete Hardy-Littlewood maximal functions

Dariusz Kosz, Mariusz Mirek, Paweł Plewa +1

Dependencies of the optimal constants in strong and weak type bounds will be studied between maximal functions corresponding to the Hardy--Littlewood averaging operators over conve…

math.CA2020

BV continuity for the uncentered Hardy--Littlewood maximal operator

Cristian González-Riquelme, Dariusz Kosz

We prove the continuity of the map $f \mapsto M f$ from $B V (R)$ to itself, where $M$ is the uncentered Hardy--Littlewood maximal operator. This answ…

math.CA2020

On differentiation of integrals in the infinite-dimensional torus

Dariusz Kosz

We answer the recently posed questions regarding the problem of differentiation of integrals for the Rubio de Francia basis $R$ in the infinite torus $T^{ω}$ . In p…

math.CA2019

Boundedness properties of maximal operators on Lorentz spaces

Dariusz Kosz

We study mapping properties of the centered Hardy--Littlewood maximal operator $M$ acting on Lorentz spaces. Given $p \in (1, \infty)$ and a metric measure space $\mathfra…

math.CA2019

BMO spaces for nondoubling metric measure spaces

Dariusz Kosz

In this article we study the family of $B M O^{p}$ spaces, $p \geq 1$ , in the general context of metric measure spaces. We give a characterization theorem that allows to describe all p…

math.CA2019★ 1 cited

Dichotomy property for maximal operators in non-doubling setting

Dariusz Kosz

We investigate a dichotomy property for Hardy--Littlewood maximal operators, non-centered $M$ and centered $M^{c}$ , that was noticed by Bennett, DeVore and Sharpley. We illustrate th…

math.CA2019

On relations between weak and strong type inequalities for modified maximal operators on non-doubling metric measure spaces

Dariusz Kosz

In this article we investigate a special class of non-doubling metric measure spaces in order to describe the possible configurations of $P_{k, s}^{c}$ , $P_{k, s}$ , $P_{k…

math.CA2019

Maximal operators on Lorentz spaces in non-doubling setting

Dariusz Kosz

We study mapping properties of the centered Hardy--Littlewood maximal operator $M$ acting on Lorentz spaces $L^{p, q} (X)$ in the context of certain non-doubling…

math.CA2018★ 4 cited

On relations between weak and restricted weak type inequalities for maximal operators on non-doubling metric measure spaces

Dariusz Kosz

In this article we study a special class of non-doubling metric measure spaces for which there is a significant difference between the incidence of weak and restricted weak type $(…

math.CA2017

On relations between weak and strong type inequalities for maximal operators on non-doubling metric measure spaces

Dariusz Kosz

In this article we characterize all possible cases that may occur in the relations between the sets of $p$ for which weak type $(p, p)$ and strong type $(p, p)$ inequalities for the…

Remarks on the Ionescu-Wainger multiplier theorem

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

On differentiation of integrals in Lebesgue spaces

The multilinear circle method and a question of Bergelson

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

Sharp constants in inequalities admitting the Calderón transference principle

Polynomial ergodic theorems in the spirit of Dunford and Zygmund

Weak-type maximal function estimates on the infinite-dimensional torus

On the doubling condition in the infinite-dimensional setting

Sharp estimates for Jacobi heat kernels in conic domains

The maximal function of the Devil's staircase is absolutely continuous

Maximal operators in nondoubling metric measure spaces

Maximal operators on the infinite-dimensional torus

A∞​ condition for general bases revisited: complete classification of definitions

Some remarks on dimension-free estimates for the discrete Hardy-Littlewood maximal functions

BV continuity for the uncentered Hardy--Littlewood maximal operator

On differentiation of integrals in the infinite-dimensional torus

Boundedness properties of maximal operators on Lorentz spaces

BMO spaces for nondoubling metric measure spaces

Dichotomy property for maximal operators in non-doubling setting

On relations between weak and strong type inequalities for modified maximal operators on non-doubling metric measure spaces

Maximal operators on Lorentz spaces in non-doubling setting

On relations between weak and restricted weak type inequalities for maximal operators on non-doubling metric measure spaces

On relations between weak and strong type inequalities for maximal operators on non-doubling metric measure spaces

$A_{\infty}$ condition for general bases revisited: complete classification of definitions