ADAM  NOWAK

Institute of Mathematics PAS

AFFILIATION  (since 2009)

    Institute of Mathematics

    Polish Academy of Sciences


FORMER AFFILIATION  (2000-2011)

    Institute of Mathematics and Computer Science

    Wrocław University of Technology


E-MAIL

    adam.nowak  at  impan.pl


SHORT CV  (more details in Polish )

  • Born: 1976, Opole, Poland
  • MSc Eng: 2000, Mathematics, Faculty of Fundamental Problems of Technology, Wrocław University of Technology
  • PhD: 2004, Mathematics, Institute of Mathematics, Wrocław University of Technology
  • Habilitation: 2008, Mathematics, Institute of Mathematics and Computer Science, Wrocław University of Technology
  • Title of professor: 2021, Natural sciences / mathematics, President of the Republic of Poland

RESEARCH INTEREST

     Harmonic analysis, Orthogonal expansions, Special functions, Integral transforms, Singular operators


SELECTED PREPRINTS

  1. A.Nowak, P.Sjögren, T.Z.Szarek,
    New sharp bounds for the Jacobi heat kernel via an extension of the Dijksma-Koornwinder formula,
    preprint 2024.  arXiv:2402.08800

PUBLICATIONS

  1. B.Langowski, A.Nowak,
    On new identities involving zeros of Bessel functions,
    J. Math. Anal. Appl. 542 (2025) 128828, 12 pp.  MR4796725
  2. B.Langowski, A.Nowak,
    On sharp heat kernel estimates in the context of Fourier-Dini expansions,
    J. Approx. Theory 304 (2024) 106103, 22 pp.  MR4805805
  3. A.Nowak, E.Sasso, P.Sjögren, K.Stempak,
    On non-centered maximal operators related to a non-doubling and non-radial exponential measure,
    Math. Ann. 388 (2024), 2887-2929.  MR4705756
  4. A.Nowak, L.Roncal, T.Z. Szarek,
    Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions,
    Commun. Pure Appl. Anal. 22 (2023), 2233-2277.  MR4608947
  5. B.Langowski, A.Nowak,
    On derivatives, Riesz transforms and Sobolev spaces for Fourier-Bessel expansions,
    J. Fourier Anal. Appl. 28 (2022), Paper No. 1, 59 pp.  MR4344837
  6. A.Nowak, P.Sjögren, T.Z.Szarek,
    Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces,
    for Jacobi expansions, on a ball and on a simplex,
    Math. Ann. 381 (2021), 1455-1476.  MR4333421
  7. B.Langowski, A.Nowak,
    Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework,
    J. Math. Anal. Appl. 499 (2021) 125061, 36 pp.  MR4216966
  8. Ó.Ciaurri, A.Nowak, L.Roncal,
    Maximal estimates for a generalized spherical mean Radon transform acting on radial functions,
    Ann. Mat. Pura Appl. 199 (2020), 1597-1619.  MR4117510
  9. A.Nowak, P.Sjögren, T.Z.Szarek,
    Sharp estimates of the spherical heat kernel,
    J. Math. Pures Appl. 129 (2019), 23-33.  MR3998788
  10. A.Arenas, E.Labarga, A.Nowak,
    Exotic multiplicity functions and heat maximal operators in certain Dunkl settings,
    Integral Transforms Spec. Funct. 29 (2018), 771-793.  MR3843030
  11. Ó.Ciaurri, A.Nowak, L.Roncal,
    Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions,
    SIAM J. Math. Anal. 49 (2017), 4402-4439.  MR3721564
  12. A.Nowak, P.Sjögren, T.Z.Szarek,
    Maximal operators of exotic and non-exotic Laguerre and other semigroups associated with classical orthogonal expansions,
    Adv. Math. 318 (2017), 307-354.  MR3689743
  13. A.Nowak, K.Stempak,
    Potential operators associated with Hankel and Hankel-Dunkl transforms,
    J. Anal. Math. 131 (2017), 277-321.  MR3631457
  14. A.Nowak, K.Stempak,
    Potential operators and Laplace type multipliers associated with the twisted Laplacian,
    Acta Math. Sci. Ser. B Engl. Ed. 37 (2017), 280-292.  MR3581541
  15. A.Nowak, K.Stempak, T.Z.Szarek,
    On harmonic analysis operators in Laguerre-Dunkl and Laguerre-symmetrized settings,
    SIGMA Symmetry Integrability Geom. Methods Appl. 12 (2016), 096, 39 pages.  MR3552207
  16. A.J.Castro, A.Nowak, T.Z.Szarek,
    Riesz-Jacobi transforms as principal value integrals,
    J. Fourier Anal. Appl. 22 (2016), 493-541.  MR3500230
  17. A.Nowak, K.Stempak,
    Sharp estimates for potential operators associated with Laguerre and Dunkl-Laguerre expansions,
    Potential Anal. 44 (2016), 109-136.  MR3455212
  18. A.Nowak, P.Sjögren, T.Z.Szarek,
    Analysis related to all admissible type parameters in the Jacobi setting,
    Constr. Approx. 41 (2015), 185-218.  MR3315675
  19. A.Nowak, L.Roncal,
    Potential operators associated with Jacobi and Fourier-Bessel expansions,
    J. Math. Anal. Appl. 422 (2015), 148-184.  MR3263453
  20. A.Nowak, K.Stempak,
    A note on recent papers by Grafakos and Teschl, and Estrada,
    J. Fourier Anal. Appl. 20 (2014), 1141-1144.  MR3254615
  21. A.Nowak, L.Roncal,
    Sharp heat kernel estimates in the Fourier-Bessel setting for a continuous range of the type parameter,
    Acta Math. Sin. (Engl. Ser.) 30 (2014), 437-444.  MR3160695
  22. A.Nowak, L.Roncal,
    On sharp heat and subordinated kernel estimates in the Fourier-Bessel setting,
    Rocky Mountain J. Math. 44 (2014), 1321-1342.  MR3274351
  23. A.Nowak, K.Stempak,
    Sharp estimates of the potential kernel for the harmonic oscillator with applications,
    Nagoya Math. J. 212 (2013), 1-17.  MR3290678
  24. A.Nowak, P.Sjögren,
    Sharp estimates of the Jacobi heat kernel,
    Studia Math. 218 (2013), 219-244.  MR3125127
  25. A.Nowak, K.Stempak,
    A symmetrized conjugacy scheme for orthogonal expansions,
    Proc. Roy. Soc. Edinburgh Sect. A 143 (2013), 427-443.  MR3039818
  26. A.Nowak, P.Sjögren,
    Calderón-Zygmund operators related to Jacobi expansions,
    J. Fourier Anal. Appl. 18 (2012), 717-749.  MR2984366
  27. J.J.Betancor, A.J.Castro, A.Nowak,
    Calderón-Zygmund operators in the Bessel setting,
    Monatsh. Math. 167 (2012), 375-403.  MR2961289
  28. A.Nowak, K.Stempak,
    On Lp-contractivity of Laguerre semigroups,
    Illinois J. Math. 56 (2012), 433-452.  MR3161334
  29. A.Nowak, T.Z.Szarek,
    Calderón-Zygmund operators related to Laguerre function expansions of convolution type,
    J. Math. Anal. Appl. 388 (2012), 801-816.  MR2869789
  30. A.Nowak, K.Stempak,
    Negative powers of Laguerre operators,
    Canad. J. Math. 64 (2012), 183-216.  MR2932174
  31. J.J.Betancor, E.Harboure, A.Nowak, B.Viviani,
    Mapping properties of fundamental operators in harmonic analysis related to Bessel operators,
    Studia Math. 197 (2010), 101-140.  MR2600427
  32. A.Nowak, L.Roncal, K.Stempak,
    Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator,
    Colloq. Math. 118 (2010), 669-684.  MR2602173
    (Contribution to the Special Volume dedicated to the memory of Professor Andrzej Hulanicki)
  33. A.Nowak, K.Stempak,
    Imaginary powers of the Dunkl harmonic oscillator,
    SIGMA Symmetry Integrability Geom. Methods Appl. 5 (2009), 016, 12 pages.  MR2481476
    (Contribution to the Special Issue on Dunkl Operators and Related Topics)
  34. A.Nowak, P.Sjögren,
    The multi-dimensional pencil phenomenon for Laguerre heat-diffusion maximal operators,
    Math. Ann. 344 (2009), 213-248.  MR2481059
  35. A.Nowak, K.Stempak,
    Riesz transforms for the Dunkl harmonic oscillator,
    Math. Z. 262 (2009), 539-556.  MR2506306
  36. A.Nowak, P.Sjögren,
    Riesz transforms for Jacobi expansions,
    J. Anal. Math. 104 (2008), 341-369.  MR2403440
  37. A.Nowak, K.Stempak,
    Relating transplantation and multipliers for Dunkl and Hankel transforms,
    Math. Nachr. 281 (2008), 1604-1611.  MR2462602
  38. O. Ciaurri, A.Nowak, K.Stempak,
    Jacobi transplantation revisited,
    Math. Z. 257 (2007), 355-380.  MR2324806
  39. A.Nowak, K.Stempak,
    Riesz transforms for multi-dimensional Laguerre function expansions,
    Adv. Math. 215 (2007), 642-678.  MR2355604
  40. A.Nowak, K.Stempak,
    Riesz transforms and conjugacy for Laguerre function expansions of Hermite type,
    J. Funct. Anal. 244 (2007), 399-443.  MR2297030
  41. A.Nowak, P.Sjögren,
    Weak type (1,1) estimates for maximal operators associated with various multi-dimensional systems of Laguerre functions,
    Indiana Univ. Math. J. 56 (2007), 417-436.  MR2305941
  42. A.Nowak, K.Stempak,
    L2-theory of Riesz transforms for orthogonal expansions,
    J. Fourier Anal. Appl. 12 (2006), 675-711.  MR2275391
  43. A.Nowak, K.Stempak,
    Weighted estimates for the Hankel transform transplantation operator,
    Tohoku Math. J. 58 (2006), 277-301.  MR2248434
  44. P.Graczyk, J.J.Loeb, I.Lopez, A.Nowak, W.Urbina,
    Higher order Riesz transforms, fractional derivatives and Sobolev spaces for Laguerre expansions,
    J. Math. Pures Appl. 84 (2005), 375-405.  MR2121578
  45. A.Nowak,
    On Riesz transforms for Laguerre expansions,
    J. Funct. Anal. 215 (2004), 217-240.  MR2085116
  46. P.Graczyk, A.Nowak,
    A composition formula for squares of Hermite polynomials and its generalizations,
    C. R. Acad. Sci. Paris Ser. I 338 (2004), 849-852.  MR2059660
  47. A.Nowak,
    Heat-diffusion and Poisson integrals for Laguerre and special Hermite expansions on weighted Lp spaces,
    Studia Math. 158 (2003), 239-268.  MR2014301
  48. K.Bogdan, T.Kulczycki, A.Nowak,
    Gradient estimates for harmonic and q-harmonic functions of symmetric stable processes,
    Illinois J. Math. 46 (2002), 541-556.  MR1936936

THESES

  • Doctoral dissertation (2004), supervisor: Prof. K.Stempak
    Poisson integrals, Riesz transforms, and conjugacy for Laguerre expansions, pp. 1-66.  MR2715713
  • Master's thesis (2000), supervisor: Dr. T.Kulczycki
    Gradient estimates of harmonic functions corresponding to symmetric stable processes, pp. 1-40.
Last update: November 2024