Harmonic analysis

Our research in harmonic analysis includes Fourier and spectral multipliers, functional inequalities, and function spaces on groups. Explore our list of publications.

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Selected publications

The following papers illustrate several directions in harmonic analysis. For further publications, see Michael Ruzhansky’s complete publication list.

Fourier multipliers and operator bounds

  • Ruzhansky M., Shaimardan S., Tulenov K., Lp-Lq boundedness of Fourier multipliers on quantum Euclidean spaces. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 120 (2026), paper no. 8.
  • Ruzhansky M., Shaimardan S., Tulenov K., Fourier multipliers and their applications to PDE on the quantum Euclidean space. NoDEA, 32 (2025), paper no. 85.
  • Ruzhansky M., Tulenov K., A note on Lp-Lq boundedness of Fourier multipliers on noncommutative spaces. Adv. Oper. Theory, 10 (2025), paper no. 48.
  • Kumar V., Ruzhansky M., Lp-Lq boundedness of (k,a)-Fourier multipliers with applications to nonlinear equations. Int. Math. Res. Not. IMRN, 2023, no. 2, 1073-1093.

Function spaces on groups

  • Hong Q., Hu G., Ruzhansky M., Fourier multipliers for Hardy spaces on graded Lie groups. Proc. Royal Soc. Edinburgh, 153 (2023), 1729-1750.
  • Cardona D., Ruzhansky M., Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups. Collect. Math., 73 (2022), 477-504.

Quantization and phase space

  • Federico S., Rottensteiner D., Ruzhansky M., Weyl calculus on graded groups. Documenta Math., 31 (2026), 1483-1540.

Our work also extends to nonharmonic analysis.