29 citations · 181 across the 37 of their papers we have counts for
25 papers · 1 filter
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…
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…
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…
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…
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…
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…
Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in
Jean Bourgain, Mariusz Mirek, Elias M. Stein +1
Dimension-free bounds will be provided in maximal and -variational inequalities on corresponding to the discrete Hardy-Littlewood averaging operators defin…
Square function estimates for discrete Radon transforms
Mariusz Mirek
We show boundedness, for , of discrete singular integrals of Radon type with the aid of appropriate square function estimates, which…
L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates
Mariusz Mirek, Elias M. Stein, Bartosz Trojan
We prove bounds for , of -variations , for discrete averaging operators and truncated singular integrals of Radon…
-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates
Mariusz Mirek, Elias M. Stein, Bartosz Trojan
We prove bounds, for , of discrete maximal functions corresponding to averaging operators and truncated singular integrals of Radon t…
A local theorem for perfect multilinear Calderón-Zygmund operators
Mariusz Mirek, Christoph Thiele
We prove a multilinear local theorem that differs from previously considered multilinear local theorems in using exclusively general testing functions as opposed…
On the Hardy--Littlewood majorant problem for arithmetic sets
Ben Krause, Mariusz Mirek, Bartosz Trojan
The aim of this paper is to exhibit a wide class of sparse deterministic sets, , so that \[ \limsup_{N \to \infty} N^{-1}|\mathbf B \cap [1,N]|= 0,…
Two-parameter version of Bourgain's inequality: Rational frequencies
Ben Krause, Mariusz Mirek, Bartosz Trojan
Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality on for the rational frequencies. We achieve this by introduc…
Variational estimates for averages and truncated singular integrals along the prime numbers
Mariusz Mirek, Bartosz Trojan, Pavel Zorin-Kranich
We prove, in a unified way, -variational estimates, , on spaces, , for averages and truncated singular integrals along the set of…
Discrete maximal functions in higher dimensions and applications to ergodic theory
Mariusz Mirek, Bartosz Trojan
We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational e…
-- boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems
Mariusz Mirek
We establish the first pointwise ergodic theorems along thin sets of prime numbers; a set with zero density with respect to the primes. For instance we will be able to achieve this…
Weak type (1, 1) inequalities for discrete rough maximal functions
Mariusz Mirek
The aim of this paper is to show that the discrete maximal function $$\mathcal{M}_{h}f(x)=\sup_{N\in\mathbb{N}}\frac{1}{|\mathbf{N}_{h}\cap[1, N]|}\Big|\sum_{n\in \mathbf{N}_{h}\ca…