Rutgers University

Department of Mathematics

Hill Center-Busch Campus

110 Frelinghuysen Road

Piscataway, NJ 08854-8019

USA

Office: Hill Center 542

Phone: 848-445-6753

E-mail: mariusz.mirek[at]rutgers.edu

I am an Assistant Professor in the Department of Mathematics at Rutgers University and

I am an Associate Professor in the Mathematical Institute at the University of Wrocław.

I was a member of the School of Mathematics at the Institute for Advanced Study in Princeton.

I completed my PhD in Mathematics at the University of Wrocław in June 2011. I obtained my

Habilitation degree from the University of Bonn in June 2016 and from the University of Wrocław

in June 2017. My research interests are concentrated in the field of harmonic analysis and its

applications to ergodic theory and probability theory.

- Assistant Professor in the Department of Mathematics at Rutgers University, (09.2018-Now).
- Lecturer in the Department of Mathematics at King's College London, (05.2017-09.2017).
- Member of the Institute for Advanced Study, Princeton, (09.2016-08.2017).
- Habilitation in Mathematics from the University of Wrocław, (20.06.2017).
- Habilitation in Mathematics from the University of Bonn, (08.06.2016).
- Associate Professor in the Mathematical Institute at the University of Wrocław, (10.2014-On leave).
- HCM Postdoctoral Research Fellowship at the University of Bonn, (10.2012-08.2016).
- Assistant Professor in the Mathematical Institute at the University of Wrocław, (10.2011-09.2014).
- PhD in Mathematics from the University of Wrocław, (07.06.2011).
- M.Sc. in Mathematics from the University of Wrocław, (05.09.2007).

- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
On discrete
Hardy--Littlewood maximal functions over the balls in $\mathbb Z^d$:
dimension-free estimates.

Accepted for publication in the Geometric Aspects of Functional Analysis. Israel Seminar (GAFA). Lecture Notes in Mathematics.

- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
On the Hardy--Littlewood
maximal functions in high dimensions: Continuous and discrete
perspective.

Accepted for publication in the Geometric Aspects of Harmonic Analysis. A conference proceedings on the occasion of Fulvio Ricci's 70th birthday Cortona, Italy, 25-29.06.2018. Springer INdAM Series.

- M. Mirek, E. M. Stein, P. Zorin-Kranich.
Jump inequalities for
translation-invariant polynomial averages and singular integrals on
$\mathbb Z^d$.

Submitted.

- M. Mirek, E. M. Stein, P. Zorin-Kranich.
A bootstrapping approach
to jump inequalities and their applications.

Accepted for publication in the Analysis & PDE.

- M. Mirek, E. M. Stein, P. Zorin-Kranich.
Jump inequalities via real
interpolation.

Accepted for publication in the Mathematische Annalen.

- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
Dimension-free estimates
for discrete Hardy-Littlewood averaging operators over the
cubes in $\mathbb Z^d$.

American Journal of Mathematics**141**, (2019), no. 4, 857-905.

- M. Mirek, E. M. Stein and B. Trojan.
$\ell^p(\mathbb Z^d)$-estimates
for discrete operators of Radon type: Maximal functions and
vector-valued estimates.

Journal of Functional Analysis**277**, (2019), no. 8, 2471-2521.

- J. Bourgain, M. Mirek, E.M. Stein and B. Wróbel.
On dimension-free
variational inequalities for averaging operators in $\mathbb R^d$.

Geometric And Functional Analysis (GAFA)**28**, (2018), no. 1, 58-99.

- M. Mirek.
Square function estimates
for discrete Radon transforms.

Analysis & PDE**11**, (2018), no. 3, 583-608.

- B. Krause, M. Mirek and B. Trojan.
Two-parameter version of
Bourgain's inequality I: Rational frequencies.

Advances in Mathematics**323**, (2018), 720-744.

- M. Mirek, E. M. Stein and B. Trojan.
$\ell^p(\mathbb Z^d)$-estimates
for discrete operators of Radon type: Variational estimates.

Inventiones Mathematicae**209**, (2017), no. 3, 665-748.

- M. Mirek, B. Trojan and P. Zorin-Kranich.
Variational estimates for
averages and truncated singular integrals along the prime numbers.

Transactions of the American Mathematical Society**369**, (2017), no. 8, 5403-5423.

- M. Mirek and C. Thiele.
A local $T(b)$ theorem for
perfect Calderón-Zygmund operators.

Proceedings of the London Mathematical Society**114**, (2017), no. 3, 35-59.

- B. Krause, M. Mirek and B. Trojan.
On the Hardy-Littlewood
majorant problem for arithmetic sets.

Journal of Functional Analysis**271**, (2016), no. 1, 164-181.

- M. Mirek and B. Trojan.
Discrete maximal functions
in higher dimensions and applications to ergodic theory.

American Journal of Mathematics**138**, (2016), no. 6, 1495-1532.

- M. Mirek and B. Trojan.
Cotlar's ergodic theorem
along the prime numbers.

Journal of Fourier Analysis and Applications**21**, (2015), no. 4, 822-848.

- M. Mirek.
Weak type $(1,1)$
inequalities for discrete rough maximal functions.

Journal d'Analyse Mathematique**127**, (2015), no. 1, 247-281.

- M. Mirek.
Roth's Theorem in the
Piatetski-Shapiro primes.

Revista Matemática Iberoamericana**31**, (2015), no. 2, 617-656.

- M. Mirek.
$\ell^p(\mathbb Z)$-boundedness
of discrete maximal functions along thin subsets of primes and
pointwise ergodic theorems.

Mathematische Zeitschrift**279**, (2015), no. 1-2, 27-59.

- M. Mirek.
Discrete
analogues in harmonic analysis: maximal functions and singular
integral operators.

Mathematisches Forschungsinstitut Oberwolfach: Real Analysis, Harmonic Analysis and Applications, 20-26 July 2014.

DOI: 10.4171/OWR/2014/34, Rep. no.**34**, (2014), 1893-1896.

- D. Buraczewski, E. Damek, S. Mentemeier and M. Mirek.
Heavy tailed solutions of
multivariate smoothing transforms.

Stochastic Processes and their Applications**123**, (2013), 1947-1986.

- M. Mirek.
On fixed points of a
generalized multidimensional affine recursion.

Probability Theory and Related Fields (2013),**156**, no. 3-4, 665-705.

- E. Damek, S. Mentemeier, M. Mirek and J. Zienkiewicz.
Convergence to stable laws
for multidimensional stochastic recursions: the case of regular
matrices.

Potential Analysis (2013),**38**no. 3, 683-697.

- D. Buraczewski, E. Damek and M. Mirek.
Asymptotics of stationary
solutions of multivariate stochastic recursions with heavy tailed
inputs and related limit theorems.

Stochastic Processes and their Applications**122**, (2012), 42-67.

- M. Mirek.
Heavy tail phenomenon and
convergence to stable laws for iterated Lipschitz maps.

Probability Theory and Related Fields**151**, (2011), no. 3, 705-734.

- M. Mirek.
Convergence
to stable laws and a local limit theorem for stochastic
recursions.

Colloquium Mathematicum**118**, (2010), 705-720.

Updated: August 20, 2019.