Oscillating multipliers on the Heisenberg group

Tom 90 / 2001

E. K. Narayanan, S. Thangavelu Colloquium Mathematicum 90 (2001), 37-50 MSC: Primary 43A80, 43A22; Secondary 42C10, 22E30. DOI: 10.4064/cm90-1-3

Streszczenie

Let ${\cal L} $ be the sublaplacian on the Heisenberg group $ H^n$. A recent result of Müller and Stein shows that the operator $ {{\cal L}}^{-1/2} \mathop {\rm sin}\nolimits \sqrt{{\cal L}} $ is bounded on $ L^p(H^n) $ for all $ p $ satisfying $ |1/p-1/2| < 1/(2n)$. In this paper we show that the same operator is bounded on $ L^p $ in the bigger range $ |1/p-1/2| < 1/(2n-1)$ if we consider only functions which are band limited in the central variable.

Autorzy

  • E. K. NarayananStatistics and Mathematics Division
    Indian Statistical Institute
    8th mile Mysore Road
    Bangalore 560 059, India
    e-mail
  • S. ThangaveluStatistics and Mathematics Division
    Indian Statistical Institute
    8th mile Mysore Road
    Bangalore 560 059, India
    e-mail

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