Leszek Skrzypczak

Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Uniwersytetu Poznańskiego 4
61-614 Poznań, Poland
Tel: +48 (61) 829-5473
lskrzyp@amu.edu.pl

Reasearch interests

  • Function spaces on Euclidean spaces, Riemaniann manifolds and Lie groups;
  • Heat semi-groups and heat kernel;
  • Properties of Sobolev and limiting embeddings;
  • Atomic and wavelet decompositions;
  • Pseudo-differential operators, their mapping and spectral properties;
  • Compact operators and their quantitative properties (entropy and s-numbers)
  • Defect of compactness, co-compactness and profile decompositions
  • Morrey spaces and smoothness Morrey spaces

Publications

  1. Embeddings of block-radial functions - approximation properties and nuclearity (with Alicja Dota ) ; arXiv: 2312.09724 https://arxiv.org/abs/2312.09724 .
  2. Embeddings of generalised Morrey smoothness spaces (with Dorothee Haroske, Zhen Liu and Susana Moura ) ; arXiv: 2310.18282 https://arxiv.org/abs/2305.00055 .
  3. Mapping properties of Fourier transforms, revisited (with Dorothee Haroske and Hans Triebel ) ; arXiv: 2310.13567 https://arxiv.org/abs/2305.00055 .
  4. On a bridge connecting Lebesgue and Morrey spaces in view of their growth properties Analysis and App. (to appear) (with Dorothee Haroske and Susana Moura ) ; arXiv: 2211.02594 https://arxiv.org/abs/2305.00055 .
  5. Nuclear embeddings of Morrey sequence spaces and smoothness Morrey spaces (with Dorothee Haroske ) ; arXiv: 2211.02594 https://arxiv.org/abs/2211.02594 .
  6. Nuclear and compact embeddings in function spaces of generalised smoothness Anal. Math. 49(2023), issue 3 https://link.springer.com/article/10.1007/s10476-023-0238-y ; (with Dorothee Haroske, Hans-Gerd Leopold and Susana Moura ) ; arXiv: 2212.12222 https://arxiv.org/abs/2212.12222v1.
  7. Limiting embeddings of Besov-type and Triebel-Lizorkin spaces on domains and an extension operator extension operator Ann. Mat. Pura Appl 202(2023) Issue 5, 2481-2516 (with Helena Goncalves and Dorothee Haroske ) https://doi.org/10.1007/s10231-023-01327-w ; arXiv: 2109.12015v1 https://arxiv.org/abs/2109.12015v1 .
  8. Nuclear Fourier transforms J. Fourier Anal.Appl. 29(3) (2023) https://doi.org/10.1007/s00041-023-10017-3 (with Dorothee Haroske and Hans Triebel ) ; arXiv: 2205.03128v1 https://arxiv.org/abs/2205.03128v1 .
  9. Nuclear embeddings in general vector-valued sequence spaces with an application to Sobolev embeddings of function spaces on quasi-bounded domains Journal of Complexity 69 (2022) 101605 https://doi.org/10.1016/j.jco.2021.101605 (with Dorothee Haroske and Hans-Gerd Leopold ) ; arXiv: 2009.00474 https://arxiv.org/abs/2009.00474 .
  10. Wavelet decomposition and embeddings of generalised Besov-Morrey spaces Nonlinear Analysis Series A: Theory, Methods & Applications 214(2022) 112590 https://www.sciencedirect.com/science/article/pii/S0362546X21002121 (with Dorothee Haroske and Susana Moura ) ; arXiv: 2009.03273 https://arxiv.org/abs/2009.03273 .
  11. Compact embeddings in Besov-type and Triebel-Lizorkin-type Spaces on bounded domains Rev. Mat. Complutense 34:761–795, (2021) <\b> (with Helena F. Goncalves and Dorothee Haroske ) doi.org/10.1007/s13163-020-00365-9 ; arXiv:2001.02046 https://arxiv.org/abs/2001.02046 .
  12. On compact subsets of Sobolev spaces on manifolds Trans. Amer. Math. Soc. 374(2021), 3761-3777 (with Cyril Tintarev ) https://doi.org/10.1090/tran/8322 ; arXiv: 2003.06456 https://arxiv.org/abs/2003.06456 .
  13. Defect of Compactness for Sobolev Spaces on Manifolds with Bounded Geometry Annali della Scuola Normale Superiore di Pisa 20(2020), 1665-1695 (with Cyril Tintarev ) DOI Number: 10.2422/2036-2145.201804_005 ; arXiv:1804.07950 https://arxiv.org/abs/1804.07950 .
  14. Nuclear embeddings in weighted function spaces Integr. Equ. Oper. Theory (2020) 92:46 doi.org/10.1007/s00020-020-02603-7 (with Dorothee Haroske ) ; doi.org/10.1090/tran/832 ; arXiv: 2002.03136 https://arxiv.org/abs/2002.03136 .
  15. Morrey Sequence Spaces: Pitt's Theorem and compact embeddings Constructive Approx. 51(2020), 505–535 (with Dorothee Haroske ) DOI:10.1007/s00365-019-09460-7 https://doi.org/10.1007/s00365-019-09460-7 ; arXiv:1807.01184 https://arxiv.org/abs/1807.01184 .
  16. Entropy numbers of compact embeddings of smoothness Morrey spaces on bounded domains Journal of Approximation Theory 256(2020) (with < Dorothee Haroske ) ; https://doi.org/10.1016/j.jat.2020.105424 ; arXiv:1902.04945 https://arxiv.org/abs/1902.04945 .
  17. Some embeddings of Morrey spaces with critical smoothness Journal of Fourier Analysis and Applications 26 (2020) DOI: 10.1007/s00041-020- 09758-2 (with Dorothee Haroske and Susana Moura ) ; arXiv:1905.09703 https://arxiv.org/abs/1905.09703 .
  18. Some properties of block-radial functions and Schroedinger type operators with block-radial potentials Journal of Comlexity 53(2019), 1-22 (with Alicja Dota ) DOI 10.1016/j.jco.2018.10.005 https://doi.org/10.1016/j.jco.2018.10.005 ; arXiv:1809.00833 https://arxiv.org/abs/1809.00833 .
  19. Some quantitative result on compact embeddings in smoothness Morrey spaces on bounded domains; an approach via interpolation FUNCTION SPACES XII. BANACH CENTER PUBLICATIONS, vol. 119, 2019, pp.181-191 (with Dorothee Haroske ).
  20. Pointwise Estimates for Block-Radial Functions of Sobolev Classes Journal of Fourier Analysis and Applications 25(2019), 321-344 (with Cyril Tintarev ) DOI:10.1007/s00041-018-9593-7 https://link.springer.com/article/10.1007/s00041-018-9593-7.
  21. Morrey spaces on domains: Different approaches and growth envelopes J. Geom. Anal. 2018, 28 No. 2, 817-841 (with Dorothee D. Haroske and Cornelia Schneider ). https://link.springer.com/article/10.1007/s12220-017-9843-y.
  22. Unboundedness properties of Smoothness Morrey spaces of regular distributions on domains Science China Mathematics 2017 Vol. 60 No. 12, 2349-2376 (with Dorothee D. Haroske, Susana Moura and Cornelia Schneider ) https://link.springer.com/article/10.1007/s11425-017-9113-9 .
  23. Compact embeddings of weighted smoothness spaces of Morrey type: an example. In: Functional Analysis, Harmonic Analysis, and Image Processing: A Collection of Paper in Honor of Bjorn Jawerth, Contemp. Math. 693, M.Cwikel, M.Milman (ed.) 2017, 235-252 (with Dorothee D. Haroske ). https://bookstore.ams.org/conm-693
  24. Embeddings of weighted Morrey spaces. Math. Nachrichten 290, No. 7, 1066-1086 (2017) / DOI 10.1002/mana.201600165 (with Dorothee D. Haroske ). https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.201600165
  25. On Caffarelli-Kohn-Nirenberg inequalities for block-radial functions Potential Anal. 2016, 45(1), 65-81 (with Cyril Tintarev ) https://arxiv.org/abs/1601.03172 , https://link.springer.com/article/10.1007/s11118-016-9535-4
  26. Smoothness Morrey Spaces of regular distributions, and some unboundedness property Nonlinear Analysis Series A: Theory, Methods & Applications 139 (2016), 218-244 (with Dorothee D. Haroske, Susana Moura ). https://www.sciencedirect.com/science/article/pii/S0362546X1600078X
  27. Embedding Properties of Besov-Type Spaces Applicable Analysis 94 (2015), no. 2, 319-341 (with Wen Yuan, Dorothee D. Haroske and Dachun Yang ).
  28. Embedding Properties of weighted Besov-Type Spaces Analysis and Applications 5 (2015), 507-553 (with Wen Yuan, Dorothee D. Haroske and Dachun Yang ). https://www.worldscientific.com/doi/pdf/10.1142/S0219530514500493 .
  29. Limiting embeddings in smoothness Morrey spaces, continuity envelopes and applications Journal of Approx. Theory 192 (2015), 306-335 (with Wen Yuan, Dorothee D. Haroske, Susana Moura, and Dachun Yang ). https://www.sciencedirect.com/science/article/pii/S0021904514002251.
  30. Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic operators. Part II. J. Math. Anal. Appl. 429 (2015), 439-460 (with Hans-Gerd Leopold ). https://www.sciencedirect.com/science/article/pii/S0022247X1500308X .
  31. On Sobolev and Franke-Jawerth embeddings of smoothness Morrey spaces Revista Mat. Complutense 27 (2014), 541 - 573 (with Dorothee D. Haroske ), https://link.springer.com/article/10.1007/s13163-013-0143-1 .
  32. Subradial functions and compact embeddings Proceedings of the Steklov Institute of Math. 284 (2014), 216 - 234, (with Winfried Sickel ).
  33. The characterization of Radial Subspaces of Besov- and Lizorkin-Triebel Spaces by Differences Function Spaces X, Conference Proceed. Banach Center Publ. 102 (2014), 216 - 234 (with Winfried Sickel and Jan Vybiral ).
  34. Complex Interpolation of weighted Besov- and Lizorkin-Triebel Spaces Acta Math. Sinica (Engl. Ser.) 30 (2014), 1297 - 1323. also: arXiv:1212.1614 (with Winfried Sickel and Jan Vybiral ).
  35. Remark on borderline traces of Besov and Triebel-Lizorkin spaces on noncompact hypersurfaces Comment. Math. 53 No. 2 (2013), 193-209, (Tomus in honorem Iuliani Musielak) (with Bernadeta Tomasz ). https://wydawnictwa.ptm.org.pl/index.php/commentationes-mathematicae/article/view/793 .
  36. Embeddings of Besov-Morrey spaces on bounded domains Studia Math. 218 (2013), 119 - 144 (with Dorothee Haroske ).
  37. A geometric criterion for compactness of invariant subspaces Archiv der Math. 101 (2013), 259–268 (with Cyril Tintarev ).
  38. Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic oparators Proc. Edinb. Math. Soc. 56 (2013), 829-851 (with Hans-Gerd Leopold ).
  39. Some s-numbers of embeddings of function spaces with weights of logarithmic type Math. Nachr. 286 (2013), 644 - 658 (with Alicja Gasiorowska ).
  40. On the Interplay of Regularity and Decay in Case of Radial Functions I. Inhomogeneous spaces, Comm. Contemp. Math. 14 (2012) 1250005 (60 pages), DOI: 10.1142/S0219199712500058 (with Winfried Sickel and Jan Vybiral ).
  41. On the Interplay of Regularity and Decay in Case of Radial Functions II. Homogeneous spaces, J.Fourier Anal. App. 18 (2012), 548-582 (with Winfried Sickel ).
  42. Continuous embeddings of Besov-Morrey function spaces Acta Math. Sin. 28 (2012), 1307 -1328 (with Dorothee Haroske ).
  43. Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, II. Genaral weghts Annales Acad. Scien. Fenn. Math. 36 (2011), 111-138 (with Dorothee D. Haroske ).
  44. Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases. Journal of Function Spaces and Applications 9 (2011), 129-178 (with Dorothee D. Haroske ).
  45. Spectral theory of some degenerate elliptic operators with local singularities, Journal of Mathematical Analysis and Applications 371 (2011) 282-299. (with Dorothee D. Haroske ).
  46. Entropy numbers of embeddings of some 2-microlocal Besov spaces Journal of Approx. Theory 163 (2011), 505-523 (with Hans-Gerd Leopold ).
  47. Corrigendum to the paper: ``On aproximation numbers of Sobolev embeddings of weighted function spaces" J. Approx. Theory 156 (2009), 116-119 (with Jan Vybiral ).
  48. Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, I Rev. Math. Complutense 21 (2008), 135-177 (with Dorothee D. Haroske ).
  49. Wavelet frames, Sobolev embeddings and negative spectrum of Schroedinger operators on manifolds with bounded geometry J. Fourier Anal. Appl. 14 (2008), 415-442.
  50. Entropy numbers of embeddings of weighted Besov spaces III. Weights of Logarithmic type, Math. Z. 255 (2007), 1-15. (with Thomas Kuehn, Hans-Gerd Leopold, Winfried Sickel ).
  51. Entropy of Sobolev embeddings of radial functions and radial eigenvalues of Schoedinger operators on isotropic manifolds Math. Nachr. 280 (2007), 654-675 (with Bernadeta Tomasz ).
  52. Approximation numbers of Sobolev embeddings of spaces of radial unctions on isotropic manifolds J. Function Spaces and Appl. 5 (2007), 27-48 (with Bernadeta Tomasz ).
  53. Entropy numbers of embeddings of weighted Besov spaces I, Constr. Approx. 23 (2006), 61-77. (with Thomas Kuehn, Hans-Gerd Leopold, Winfried Sickel ).
  54. Entropy numbers of embeddings of weighted Besov spaces II, Proc. Edinb. Math. Soc. 49 (2006), 331-359. (with Thomas Kuehn, Hans-Gerd Leopold, Winfried Sickel ).
  55. Approximation and entropy numbers of compact Sobolev embeddings. Approximation and Probability. Banach Center Publications vol.72, Warszawa 2006, pp.309-326.).
  56. Smoothing properties and compactness of Riesz-Bessel potentials on symmetric spaces on noncompact type. In: Harmonic Analysis and Applications. Procc. of Inter. Conf. Osaka 2004, Yokohama Publishers 2006, pp.77-90.).
  57. On Approximation numbers of Sobolev embeddings of weighted function spaces. J. Approx. Theory 136(2005), 91-107.
  58. Entropy numbers of Trudinger-Strichartz embeddings of radial Besov spaces and applications, J. London Math.Soc. 69 (2004), 465-488
  59. Approximation numbers of Sobolev embeddings of spaces of radial functions Comment. Math. Tomus specialis in honorem Iuliani Musielak (2004), 238-255. (with Bernadeta Tomasz ).
  60. Heat extensions, optimal atomic decompositions and Sobolev embeddings on in presence of symmetries on manifolds, Math. Zeitsch. 243 (2003), 745-773
  61. Entropy numbers of Sobolev embeddings of radial Besov spaces, J.Approx.Theory 121 (2003), 244-268. (with Thomas Kuehn, Hans-Gerd Leopold, Winfried Sickel ).
  62. Entropy numbers of embeddings of weighted Besov spaces, Jenaer Schriften zur Mathematik und Informatik 13/03 (2003), 1-57. (with Thomas Kuehn, Hans-Gerd Leopold, Winfried Sickel ).
  63. Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay properties, Revista Mat. Iberoamer. 18 (2002), 267-299.
  64. Besov spaces and Hausdorff dimension for some Carnot-Carath\'eodory metric spaces, Canadian J. of Math. 54 (2002), 1280-1304.
  65. Compactness of embeddings of the Trudinger-Strichartz type for rotation invariant function, Huston J. Math. 27 (2001), 633-647. (with Bernadeta Tomasz ).
  66. Remarks on twisted product in Besov, In: Function Spaces. The fifth conference Marcel Dekker, Inc., New York-Basel, 2000, pp.475-487.
  67. Radial subspaces of Besov and Lizorkin-Triebel classes: extended Strauss lemma and compactness of embeddings, J.Fourier Anal. App. 6 (2000), 639-662. (with Winfried Sickel ).
  68. Heat and harmonic extensions for function spaces of Hardy-Sobolev-Besov type on symmetric spaces and Lie groups, J. Approx. Theory 96 (1999), 149-170.
  69. Spherical transform and Besov spaces on semisimple Lie groups, Functiones et Approximatio 26 (1998), 181-187.
  70. The atomic decomposition on manifolds with bounded geometry, Forum Math. 10 (1998), 19-38.
  71. The Triebel-Lizorkin scale of function spaces for Fourier-Helgason transform, Math. Nachr. 190 (1998), 251- 274.
  72. Mapping properties of pseudodifferential operators on manifolds with bounded geometry, J. London Math. Soc. 57 (1998), 721-738.
  73. Besov spaces on symmetric manifolds - the atomic decomposition, Studia Math. 124 (1997), 215-238.
  74. Some equivalent norms in Sobolev and Besov spaces on symmetric manifolds, J. London Math. Soc. 53 (1996), 569-581.
  75. Besov spaces on symmetric manifolds, Hokkaido Math. J. 25 (1996), 231-247.
  76. Heat semi--group and Function spaces on symmetric spaces of the noncompact type, Zeitsch. Anal. ihre Anwend. 15 (1996), 881-899.
  77. Vector-valued Fourier multipliers on symmetric spaces of the non-compact type , Monatshefte Math. 119 (1995), 99--123.
  78. Besov spaces and function series on Lie groups II, Collect.Math. 44 (1993), 271 - 279.
  79. Besov spaces and function series on Lie groups, Comm.Math.Univ.Carolinae 34 (1993), 139-147.
  80. Remark on pointwise multipliers for Triebel scales on Riemannian manifolds, Functiones et Approximatio 21 (1992), 3-6.
  81. Anisotropic Sobolev spaces on Riemannian symmetric manifolds, II. Intermediate spaces, Comm.Math. 31 (1991) 165-178.
  82. Anisotropic Sobolev spaces on Riemannian symmetric manifolds, in: Function Spaces. Proc. II Inter.Conf. Poznan, Teubner-Texte zur Mathematik, Leipzig 1991, 252-264.
  83. Function spaces of Sobolev type on Riemannian symmetric manifolds, Forum Math. 3 (1991), 339-353.
  84. Traces of function spaces of $F^{s}_{p,q}-B^{s}_{p,q}$ type on submanifolds, Math.Nachr. 146 (1990), 137-147.
  85. Remark on spline unconditional bases in $H^{1}(D)$, In: Approximation and Function Spaces. Banach Center Publication 22 , PWN Warsaw 1989, 427-433.

Duty hours and further information

Duty hours:
Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Room B1-42
Uniwersytetu Poznańskiego 4,
61-614, Poznań, Poland
Tuesday: 12.00 – 13.00
Wednesday: 10.30 – 11.30

News:

Learning modules

Fourier series and integrals

The aim of the module is to present the basic and the most important facts concerning the Fourier series of periodic function and Fourier transform defined on real line. Finishing the course students will know the basic concepts of the theory of Fourier series and Fourier transform of functions of one-variable. They can used Fourier series and transform to solve different mathematical problems as well as some problems arising in natural sciences.

Fourier series and integrals- learning module description

From polynomials to wavelets: introduction to the theory of approximation

The aim of the module is to introduce the main concepts and ideas of modern approximation theory. However, the classical approximation results will also be presented as a background and motivation for the modern concepts. After the course the student should be able to use main approximation schemes in different mathematical problems and in application.

From polynomials to wavelets: introduction to the theory of approximation-learning module description

Distributions, Fourier Transform and PDE

The theory of distributions was a breakthrough point in the development in mathematical analysis in XX century. The theory find the crucial applications in partial differential equations, harmonic analysis, representation theory of Lie groups ect. The aim of the module is to introduce the main concepts and ideas of the theory of distributions and the main scheme of its applications to partial differential equations. After the course the student should be able to use distributions as a tool and environment to solve different problems in mathematical analysis in particular in PDE.

Distributions, Fourier Transform and PDE - -learning module description

Harmonic Analysis

The aim of the module is the presentation of main ideas of harmonic analysis. It will be described how the ideas are realized for functions defined on Euclidean spaces $\R^d$. The main concepts of the harmonic analysis on $\R^d$ will defined, the relation among them will described as well as their applications.

Harmonic Analysis-learning module description

Introduction to Wavelets

Wavelet analysis was created in 70-ties last century as a method of expansion of functions in to series. It is an alternative method to the classical method of representation functions via Fourier series. Wavelet expansions are the expansion with respect to the family of functions, that is constructed from a single function via translations and dilatations. Functions that give us a ``good’’ expansions constructed in that way are called wavelets. The wavelets theory quickly appeared very useful tool in many applications in mathematics, physics and computer science (e.g. signal processing, image compression). The aim of the module is to introduce the mathematical background of the wavelets.

Introduction to wavelets-learning module description

Description of the learning modules given in Polish

Description of the learning modules given in Polish can be found at the Polish version of this side.

Contact

Faculty of Mathematics and Computer Science
Adam Mickiewicz University
ul. Uniwersytetu Poznańskiego 4
61-614 Poznań, Poland
Phone: +48 (61) 829-5473
e-mail: lskrzyp@amu.edu.pl