Functional Analysis and Its Applications

, Volume 47, Issue 1, pp 72–75 | Cite as

On multipliers on compact Lie groups

  • M. V. RuzhanskyEmail author
  • J. Wirth


In this note we announce L p multiplier theorems for invariant and noninvariant operators on compact Lie groups in the spirit of the well-known Hörmander-Mikhlin theorem on ℝ n and its versions on the torus \(\mathbb{T}^n\). Applications to mapping properties of pseudo-differential operators on L p -spaces and to a priori estimates for nonhypoelliptic operators are given.

Key words

multiplier pseudo-differential operator Lie group 


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  1. [1]
    R. Coifman and M. de Guzman, Rev. Un. Mat. Argentina, 25 (1970/71), 137–143.MathSciNetzbMATHGoogle Scholar
  2. [2]
    R. Coifman and G. Weiss, Rev. Un. Mat. Argentina, 25 (1970/71), 145–166.MathSciNetzbMATHGoogle Scholar
  3. [3]
    R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogenes, Springer-Verlag, 1971.zbMATHGoogle Scholar
  4. [4]
    L. Hörmander, Acta Math., 104 (1960), 93–140.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    S. G. Mihlin, Dokl. Akad. Nauk SSSR, 109 (1956), 701–703.MathSciNetGoogle Scholar
  6. [6]
    S. G. Mihlin, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr., 12: 7 (1957), 143–155.MathSciNetGoogle Scholar
  7. [7]
    M. Ruzhansky and V. Turunen, Pseudo-Differential Operators and Symmetries, Birkhäuser, Basel, 2010.zbMATHCrossRefGoogle Scholar
  8. [8]
    M. Ruzhansky, V. Turunen, and J. Wirth,
  9. [9]
    M. Ruzhansky and J. Wirth,

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Imperial College LondonLondonUK
  2. 2.University of StuttgartStuttgartUK

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