Title: Spherical-Radial Multipliers on the Heisenberg Group
Author(s): M.E. Egwe
Pages: 718-723
Cite as:
M.E. Egwe, Spherical-Radial Multipliers on the Heisenberg Group, Int. J. Anal. Appl., 18 (5) (2020), 718-723.


Let Hn be the (2n+1)-dimensional Heisenberg group. We consider a radial Fourier multiplier which is a spherical function on Hn and show that it is a Herz-Schur multiplier.

Full Text: PDF



  1. B. Astengo, D.B. Blasio, and F. Ricci. Gelfand Pairs on the Heisenberg Group and Schwartz Functions. J. Funct. Anal. 256 (5) (2009), 1565-1587. Google Scholar

  2. S. Bagchi. Fourier Multipliers on the Heisenberg groups revisited arXiv:1710.02822v2 [math.CA], 2017. Google Scholar

  3. C. Benson, J. Jenkins. Bounded K-Spherical Functions on the Heisenberg Groups.J. Funct. Anal. 105 (1992), 409-443. Google Scholar

  4. M. Bozejko, G. Fendler. Herz-Schur multipliers and uniformly bounded representations of discrete groups, Arch. Math. 57 (1991), 290-298. Google Scholar

  5. M.E. Egwe. Aspects of Harmonic Analysis on the Heisenberg group. Ph.D. Thesis, University of Ibadan, Ibadan, Nigeria, 2010. Google Scholar

  6. M.E. Egwe, U.N. Bassey. On Isomorphism Between Certain Group Algebras on the Heisenberg Group, J. Math. Phys. Anal. Geom. 9 (2) (2013), 150-164. Google Scholar

  7. M.E. Egwe. A K-Spherical-Type Solution for Invariant Differential Operators on the Heisenberg Group. Int. J. Math. Anal. 8 (30) 2014, 1475-1486. Google Scholar

  8. M.E. Egwe. The Equivalence of certain norms on the Heisenber group. Adv. Pure Math. 3 (6) (2013), 576-578. Google Scholar

  9. G.B. Folland, Harmonic analysis in phase space, Princeton University Press, Princeton, N.J, 1989. Google Scholar

  10. R. Gangolli. Spherical Functions on Semisimple Lie Groups. In: Symmetric Spaces, W. Boothy and G. Weiss (Eds.). Marcel Dekker, Inc. New York, 1972. Google Scholar

  11. S. Helgason, Groups and geometric analysis: integral geometry, invariant differential operators, and spherical functions, Academic Press, Orlando, 1984. Google Scholar

  12. R. Howe. On the role of the Heisenberg group in harmonic analysis. Bull. Amer. Math. Soc. 3 (1980), 821-843. Google Scholar

  13. G. Mauceri. Lp-Multipliers on the Heisenberg group. Michigan Math. J. 26 (1979), 361-371. Google Scholar

  14. F. Ricci. Fourier and Spectral Multipliers in RN and in the Heisenberg group. http://homepage.sns.it/fricci/papers/ multipliers.pdf Google Scholar

  15. F. Ricci, R.L. Rubin. Transferring Fourier Multipliers from SU(2) to the Heisenberg Group. Amer. J. Math. 108 (3) (1986), 571-588. Google Scholar

  16. S. Thangavelu. Spherical Means on the Heisenberg Group and a Restriction Theorem for the Symplectic Fourier Transform. Revista Math. Iberoamericana 7 (2) (1991), 135-165. Google Scholar

  17. S. Thangavelu, Harmonic Analysis on the Heisenberg Group, Birkh¨auser Boston, Boston, MA, 1998. Google Scholar


Copyright © 2020 IJAA, unless otherwise stated.