Aidyn Kassymov

I am a postdoctoral researcher at Ghent University. Previously, I was the PhD student with the joint program between Ghent University and Al-Farabi Kazakh National University.
My supervisors are Professor Michael Ruzhansky and Assoc. Professor Durvudkhan Suragan. I am interested in harmonic analysis, sub-elliptic functional inequalities, spectral geometry and PDE.  My work concerns mainly in the functional inequalities on Lie groups and its applications to PDE.

The list of publications:

  1. Kassymov A., Ruzhansky M., Suragan D., Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups, arxiv
  2. Kassymov A., Ruzhansky M., Suragan D., Reverse integral Hardy inequalities on metric measure spaces. arxiv
  3. Kassymov A., Ruzhansky M., Suragan D., Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and p-sub-Laplacian systems. arxiv
  4. Kassymov A., Ruzhansky M., Suragan D., Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups. NoDEA Nonlinear Differential Equations Appl., to appear. link
  5. Kassymov, Aidyn; Ruzhansky, Michael; Suragan, Durvudkhan Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups. Integral Transforms Spec. Funct. 30 (2019), no. 8, 643–655.
  6. Kal’menov, Tynysbek Sh.; Kassymov, Aidyn; Suragan, Durvudkhan Isoperimetric inequalities for the heat potential operator. Filomat 32 (2018), no. 3, 903–910.
  7. Kal’menov, Tynysbek Sh.; Kassymov, Aidyn; Suragan, Durvudkhan Isoperimetric inequalities for the Cauchy-Dirichlet heat operator. Filomat 32 (2018), no. 3, 885–892.
  8. Tulenov, Kanat Serikovich; Akhymbek, Meiram Erkanatuly; Kassymov, Aidyn Adilovich Clarkson inequalities on Lp(Gˆ) space associated with compact Lie group. J. Pseudo-Differ. Oper. Appl. 9 (2018), no. 2, 443–450.
  9. Kassymov, Aidyn; Suragan, Durvudkhan Some spectral geometry inequalities for generalized heat potential operators. Complex Anal. Oper. Theory 11 (2017), no. 6, 1371–1385.
  10. Kassymov, A.; Sadybekov, M.; Suragan, D. On isoperimetric inequalities for the Cauchy-Robin heat operator. Math. Model. Nat. Phenom. 12 (2017), no. 3, 114–118.
  11. Kal’menov, Tynysbek; Kassymov, Aidyn; Suragan, Durvudkhan On s-number inequalities of triangular cylinders for the heat operator. Functional analysis in interdisciplinary applications, 349–362, Springer Proc. Math. Stat., 216, Springer, Cham, 2017.