29 citations · 181 across the 37 of their papers we have counts for
43 papers
Dimension-free estimates for discrete maximal functions over cubes in
Mariusz Mirek, Tomasz Z. Szarek, Błażej Wróbel
In this short note, we establish dimension-free bounds, for all , for the discrete Hardy--Littlewood maximal functions associated with cubes i…
Pointwise ergodic theorems along sequences of intermediate growth
Leonidas Daskalakis, Mariusz Mirek, Máté Wierdl
We establish the first pointwise convergence result for ergodic averages with iterates along explicit and deterministic sequences of intermediate growth, that is, growing faster th…
Discrete analogues in harmonic analysis: Multi-parameter Radon averages
Agnieszka Hejna-Łyżwa, Joonil Kim, Bartosz Langowski +3
In this paper we study maximal and oscillation inequalities for multi-parameter discrete Radon averaging operators. We develop a robust variant of the multi-parameter circle method…
A remark on Kolmogorov's theorem
Arash Lotfi, Mariusz Mirek, Richard K. Yu
The aim of this note is to illustrate that the set of integrable functions on the torus for which the Fourier series diverges almost everywhere is of the second Baire…
Discrete analogues in harmonic analysis: methods
Bartosz Langowski, Mariusz Mirek, Tomasz Z. Szarek
In this note we present how the almost-orthogonality methods based on arguments can be employed to study boundedness of discrete operators of Radon type. Almost-orthogonalit…
Pointwise convergence of polynomial multiple ergodic averages along the primes
Mariusz Mirek, Renhui Wan, James Wright
We establish pointwise almost everywhere convergence for the polynomial multilinear ergodic averages $$\frac{1}{N} \sum_{n=1}^N \La(n) f_1(T^{P_1(n)} x)\cdots f_k(T^{P_k(n)} x)$$ a…
Dimension-free estimates for discrete maximal functions related to normalized sampled gaussians
Mariusz Mirek, Tomasz Z. Szarek, Błażej Wróbel
In this paper, we investigate dimension-free estimates for convolution operators with discrete normalized sampled Gaussians (related to the Theta function) in the context of maxima…
The multilinear circle method and a question of Bergelson
Dariusz Kosz, Mariusz Mirek, Sarah Peluse +2
Let and be a probability space equipped with a family of commuting invertible measure-preserving transformations $T_1,\ldots, T_k \colon…
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 , , for certain multiparameter polynomial ergodic averages in th…
Polynomial sequences in discrete nilpotent groups of step 2
Alexandru D. Ionescu, Akos Magyar, Mariusz Mirek +1
We discuss some of our work on averages along polynomial sequences in nilpotent groups of step 2. Our main results include boundedness of associated maximal functions and singular…
Polynomial progressions in topological fields
Ben Krause, Mariusz Mirek, Sarah Peluse +1
Let be polynomials with distinct degrees, no constant terms and coefficients in a general locally compact topological field . We give a quantitative…
Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives
Mariusz Mirek, Tomasz Z. Szarek, James Wright
In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention…
On a multi-parameter variant of the Bellow-Furstenberg problem
Jean Bourgain, Mariusz Mirek, Elias M. Stein +1
We prove convergence in norm and pointwise almost everywhere on , , for certain multi-parameter polynomial ergodic averages by establishing the corresponding…
Polynomial averages and pointwise ergodic theorems on nilpotent groups
Alexandru D. Ionescu, Ákos Magyar, Mariusz Mirek +1
We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on -fi…
Some remarks on oscillation inequalities
Mariusz Mirek, Wojciech Słomian, Tomasz Z. Szarek
In this paper we establish uniform oscillation estimates on with for the polynomial ergodic averages. This result contributes to a certain problem about u…
Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres
Alex Iosevich, Bartosz Langowski, Mariusz Mirek +1
We establish an asymptotic formula for the number of lattice points in the sets \[ \mathbf S_{h_1, h_2, h_3}(λ): =\{x\in\mathbb Z_+^3:\lfloor h_1(x_1)\rfloor+\lfloor h_2(x_2)\rfloo…
Dimension-free estimates for the discrete spherical maximal functions
Mariusz Mirek, Tomasz Z. Szarek, Błażej Wróbel
We prove that the discrete spherical maximal functions (in the spirit of Magyar, Stein and Wainger) corresponding to the Euclidean spheres in with dyadic radii have $…
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…
Pointwise ergodic theorems for non-conventional bilinear polynomial averages
Ben Krause, Mariusz Mirek, Terence Tao
We establish convergence in norm and pointwise almost everywhere for the non-conventional (in the sense of Furstenberg) bilinear polynomial ergodic averages \[ A_N(f,g)(x) := \frac…
On discrete Hardy-Littlewood maximal functions over the balls in : dimension-free estimates
Jean Bourgain, Mariusz Mirek, Elias M. Stein Błażej Wróbel
We show that the discrete Hardy-Littlewood maximal functions associated with the Euclidean balls in with dyadic radii have bounds independent of the dimension on $\el…
On the Hardy--Littlewood maximal functions in high dimensions: Continuous and discrete perspective
Jean Bourgain, Mariusz Mirek, Elias M. Stein +1
This is a survey article about recent developments in dimension-free estimates for maximal functions corresponding to the Hardy--Littlewood averaging operators associated with conv…
Jump inequalities for translation-invariant operators of Radon type on
Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
We prove strong jump inequalities for a large class of operators of Radon type in the discrete and ergodic theoretical settings. These inequalities are the endpoints of the $…
A bootstrapping approach to jump inequalities and their applications
Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
The aim of this paper is to present an abstract and general approach to jump inequalities in harmonic analysis. Our principal conclusion is the refinement of -variational estima…
Jump inequalities via real interpolation
Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
Jump inequalities are the endpoint of Lépingle's inequality for -variation of martingales. Extending earlier work by Pisier and Xu we interpret these inequalities in terms…