JournalsrmiVol. 20, No. 2pp. 517–530

The Singularity of Orbital Measures on Compact Lie Groups

  • Kathryn E. Hare

    University of Waterloo, Waterloo, Canada
  • Wai Ling Yee

    Massachusetts Institute of Technology, Cambridge, USA
The Singularity of Orbital Measures on Compact Lie Groups cover
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Abstract

We find the minimal real number kk such that the kkth power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to l2l^{2}. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of LpL^{p}-improving measures.

Cite this article

Kathryn E. Hare, Wai Ling Yee, The Singularity of Orbital Measures on Compact Lie Groups. Rev. Mat. Iberoam. 20 (2004), no. 2, pp. 517–530

DOI 10.4171/RMI/399