Błażej Wróbel


Mathematical Institute
Plac Grunwaldzki 2/4
50-384 Wrocław
POLAND

Contact:



Office: 10.2
Phone: +48 71 37 57 401
E-mail: blazej.wrobel[at]math.uni.wroc.pl or blazej.wrobel[at]uwr.edu.pl

About me:

I am an associate professor in the Mathematical Institute at the University of Wrocław and an associate professor at the Institute of Mathematics of the Polish Academy of Sciences.
I completed my PhD in Mathematics in 2014 via a co-tutelle agreement beetween the University of Wrocław and Scuola Normale Superiore, Pisa. My PhD thesis was entitled 'Multivariate Spectral Multipliers' and it is avaliable here .
I obtained my Habilitation degree from the University of Wrocław in June 2019.

The main area of my research is harmonic analysis. I am especially interested in high-dimensional phenomena that arise as the dimension tends to infinity. I am also interested in related aspects of operator theory, PDE, analytic number theory, and ergodic theory.

Education and employment:


Papers:

  1. M. Kucharski, B. Wróbel, J. Zienkiewicz. Dimension-free $L^p$ estimates for higher order maximal Riesz transforms in terms of the Riesz transforms
    submitted 06.2023.

  2. B. Wróbel Improved multiplier theorems on rank one noncompact symmetric spaces
    submitted 05.2023.

  3. M. Kucharski, B. Wróbel, J. Zienkiewicz. Dimension-free $L^p$ estimates for odd order maximal Riesz transforms in terms of the Riesz transforms
    submitted 06.2022.

  4. M. Kucharski and B. Wróbel. On $L^p$ estimates for positivity-preserving Riesz transforms related to Schrödinger operators
    submitted 03.2022.

  5. J. Mirek, W. Słomian, and B. Wróbel. On the solution of Warring Problem with a multiplicative error term: dimension free estimates
    accepted in Proceedings of the AMS, 01.2023 .

  6. M. Mirek, T. Z. Szarek, and B. Wróbel. Dimension-free estimates for the discrete spherical maximal functions,
    IMRN, online first 01.2023, https://doi.org/10.1093/imrn/rnac329 .

  7. M. Kucharski and B. Wróbel. A dimension-free estimate on $L^2$ for the maximal Riesz transform in terms of the Riesz transform
    Math. Annalen, online first 06.2022, https://doi.org/10.1007/s00208-022-02417-5 .

  8. D. Kosz, M. Mirek, P. Plewa, and B. Wróbel. Some remarks on dimension-free estimates for the discrete Hardy-Littlewood maximal functions,
    Israel J. Math. online first 11.2022, https://doi.org/10.1007/s11856-022-2382-7.

  9. S. Meda and B. Wróbel. Marcinkiewicz-type multipliers on products of noncompact symmetric spaces
    Annali della Scuola normale superiore di Pisa - Classe di scienze, (4) 22 (2021).

  10. J. Bourgain, M. Mirek, E.M. Stein, and B. Wróbel. On the Hardy-Littlewood maximal functions in high dimensions: Continuous and discrete perspective
    In: Ciatti P., Martini A. (eds) Geometric Aspects of Harmonic Analysis. Springer INdAM Series, vol 45, 2021, Springer.

  11. J. Bourgain, M. Mirek, E.M. Stein, and B. Wróbel. On discrete Hardy-Littlewood maximal functions over the balls in $Z^d$: dimension-free estimates
    Geometric Aspects of Functional Analysis – Israel Seminar (GAFA) 2017-2019, Lecture Notes in Mathematics 2256 (2020).

  12. F. Ricci and B. Wróbel. Spectral multipliers for functions of fixed $K$-type on $SL(2,\mathbb{R}).$
    Math. Nachrichten, (3) 293 (2020)

  13. J. Bourgain, M. Mirek, E.M. Stein, and B. Wróbel. Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in $\mathbb{Z}^d.$
    Amer. J. Math. (4) 141 (2019)

  14. D. Celotto, S. Meda, and B. Wróbel. $L^p$ spherical multipliers on homogenous trees.
    Studia Math. 247 (2019), 175-190.

  15. 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 (1), (2018), 58-99.

  16. B. Wróbel. Approaching bilinear multipliers via a functional calculus.
    J. Geom. Anal. 28 (2018), 3048–3080.

  17. B. Wróbel. Dimension-free $L^p$ estimates for vectors of Riesz transforms associated with orthogonal expansions.
    Analysis & PDE. 11 (3), (2018), 745–773.

  18. B. Wróbel. On the consequences of a Mihlin-Hörmander functional calculus: square function and maximal function estimates.
    Math. Zeitschrift 287 (1-2), (2017), 143–153.

  19. B. Wróbel. Joint spectral multipliers for mixed systems of operators.
    J. Fourier Anal. Appl. 23 (2), (2017), 245-287.

  20. J. Dziubański, B. Wróbel. Strong continuity on Hardy spaces.
    J. Approx. Th. 211, (2016), 85–93.

  21. B. Wróbel. Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator.
    Forum Math. 27 (4), (2015), 2301-–2322.

  22. B. Wróbel. Dimension free $L^p$ estimates for single Riesz transforms via an $H^{\infty}$ joint functional calculus.
    J. Funct. Anal. 267 (9), (2014), 3332-3350.

  23. B. Wróbel. Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators.
    Studia Math. 216 , (2013), 47-67.

  24. B. Wróbel. Laplace type multipliers for Laguerre function expansions of Hermite type.
    Mediterr. J. Math. 10 (4), (2013), 1867-1881.

  25. J. Dziubański, M. Preisner, and B. Wróbel. Multivariate Hörmander-type multiplier theorem for the Hankel transform.
    J. Fourier Anal. Appl. 19, (2013), 417-437.

  26. K. Stempak and B. Wróbel. Dimension free $L^p$ estimates for Riesz transforms associated with Laguerre function expansions of Hermite type.
    Taiwanese J. Math. 17, (2013), 63-81.

  27. B. Wróbel. Multivariate spectral multipliers for tensor product orthogonal expansions.
    Monatsh. Math. 168 (1), (2012), 125-149, Erratum.

  28. B. Wróbel. On g-functions for Laguerre function expansions of Hermite type.
    Proc. Ind. Acad. Sc., Math. Sc. 121, (2011), 45-75.

  29. B. Wróbel. Imaginary powers of a Laguerre differential operator.
    Acta Math. Hungar. 124, (2009), 333-351.

Last updated: 05.07.2022