Mathematische Zeitschrift

, Volume 267, Issue 1–2, pp 235–259

Central oscillating multipliers on compact Lie groups



Fefferman and Stein and Wainger proved optimal Lp boundedness for certain oscillating multipliers on \({\mathbb{R}^{d}}\). In this article, we prove analogues of their results for a compact Lie group.


Oscillating multiplier Lp spaces Hp spaces Compact Lie groups Fourier series 

Mathematics Subject Classification (2000)

43A22 43A32 43B25 42B25 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alexopoulos G.: Oscillating multipliers on Lie groups and Riemannian manifolds. Tohoku Math. J. 46, 457–468 (1994)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Blank B., Fan D.: H p spaces on compact Lie groups. Ann. Fac. Sci. Toulouse Math. 6(6), 429–479 (1997)MATHMathSciNetGoogle Scholar
  3. 3.
    Bloom W.R., Xu Z.: Approximation of H p functions by Bochner–Riesz means on compact Lie groups. Math. Z. 216, 131–145 (1994)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Clerc J.L.: Bochner–Riesz means of H p functions (0 < p < 1) on compact Lie groups. Lect. Notes Math. 1234, 86–107 (1987)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Colzani, L.: Hardy space on sphere. Ph.D. Thesis, Washington University, St Louis (1982)Google Scholar
  6. 6.
    Chen S., Wang J.: Decomposition of BMO functions on normal groups. Acta Math. Sin. 32, 345–357 (1989)MATHGoogle Scholar
  7. 7.
    Coifman R., Weiss G.: Extension of hardy spaces and their use in analysis. Bull. Am. Math. Soc. 83, 569–645 (1977)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Domar Y.: On the spectral synthesis problem for (n−1)-dimensional subset of R n, n ≥ 2. Ark Math. 9, 23–37 (1971)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chen, J., Fan, D.: A bilinear fractional integral on compact Lie groups. Can. Math. Bull (to appear)Google Scholar
  10. 10.
    Cowling M., Mantero A.M., Ricci F.: Pointwise estimates for some kernels on compact Lie groups. Rend. Circ. Mat. Palerma XXXI, 145–158 (1982)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Fan D.: Calderón-Zygmund operators on compact Lie groups. Math. Z. 216, 401–415 (1994)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Fefferman C., Stein E.M.: H p space of several variables. Acta Math. 129, 137–193 (1972)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Giulini S., Meda S.: Oscillating multiplier on noncompact symmetric spaces. J. Reine Angew. Math. 409, 93–105 (1990)MATHMathSciNetGoogle Scholar
  14. 14.
    Latter R.H.: A characterization of \({H^{p}(\mathbb{R}^{n})}\) in terms of atoms. Stud. Math. 62, 93–101 (1978)MATHMathSciNetGoogle Scholar
  15. 15.
    Littman W.: Fourier transforms of surface-carried measures and differentiability of surface average. Bull. Am. Math. Soc. 69, 766–770 (1963)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Marias M.: L p-boundedness of oscillating spectral multipliers on Riemannian manifolds. Ann. Math. 10, 133–160 (2003)MATHMathSciNetGoogle Scholar
  17. 17.
    Miyachi A.: On some singular Fourier multipliers. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28(2), 267–315 (1981)MATHMathSciNetGoogle Scholar
  18. 18.
    Sjölin P.: An H p inequality for strongly singular integrals. Math. Z. 165, 231–238 (1979)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Stein E.M.: Topics in Harmonic Analysis. Annals of Mathematics Studies #63. Princeton University Press, Princeton (1970)Google Scholar
  20. 20.
    Stein E.M., Weiss G.: Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton (1971)MATHGoogle Scholar
  21. 21.
    Wainger, S.: Special trigonometric series in k dimensions. Mem. Am. Math. Soc. 59 (1965)Google Scholar
  22. 22.
    Watson G.N.: A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge (1922)MATHGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.Department of MathematicsUniversity of Wisconsin-MilwaukeeMilwaukeeUSA

Personalised recommendations