29 citations · 181 across the 37 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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…
Cotlar's ergodic theorem along the prime numbers
Mariusz Mirek, Bartosz Trojan
The aim of this paper is to prove Cotlar's ergodic theorem modeled on the set of primes.