Transferring L p multipliers

Anthony H. Dooley

Annales de l'institut Fourier (1986)

  • Volume: 36, Issue: 4, page 107-136
  • ISSN: 0373-0956

Abstract

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By combining some results of C. S. Herz on the Fourier algebra with the notion of contractions of Lie groups, we prove theorems which allow transference of L p multipliers either from the Lie algebra or from the Cartan motion group associated to a compact Lie group to the group itself.

How to cite

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Dooley, Anthony H.. "Transferring $L^p$ multipliers." Annales de l'institut Fourier 36.4 (1986): 107-136. <http://eudml.org/doc/74731>.

@article{Dooley1986,
abstract = {By combining some results of C. S. Herz on the Fourier algebra with the notion of contractions of Lie groups, we prove theorems which allow transference of $L^ p$ multipliers either from the Lie algebra or from the Cartan motion group associated to a compact Lie group to the group itself.},
author = {Dooley, Anthony H.},
journal = {Annales de l'institut Fourier},
keywords = {Fourier algebra; contractions of Lie groups; multipliers; Cartan motion group},
language = {eng},
number = {4},
pages = {107-136},
publisher = {Association des Annales de l'Institut Fourier},
title = {Transferring $L^p$ multipliers},
url = {http://eudml.org/doc/74731},
volume = {36},
year = {1986},
}

TY - JOUR
AU - Dooley, Anthony H.
TI - Transferring $L^p$ multipliers
JO - Annales de l'institut Fourier
PY - 1986
PB - Association des Annales de l'Institut Fourier
VL - 36
IS - 4
SP - 107
EP - 136
AB - By combining some results of C. S. Herz on the Fourier algebra with the notion of contractions of Lie groups, we prove theorems which allow transference of $L^ p$ multipliers either from the Lie algebra or from the Cartan motion group associated to a compact Lie group to the group itself.
LA - eng
KW - Fourier algebra; contractions of Lie groups; multipliers; Cartan motion group
UR - http://eudml.org/doc/74731
ER -

References

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  2. [2] J. L. CLERC, Une formule asymptotique du type Mehler-Heine pour les zonales d'un espace riemannien, Studia Math., 57 (1976), 27-32. Zbl0335.43010MR54 #13476
  3. [3] R. R. COIFMAN and G. WEISS, Analyse harmonique sur certains espaces homogènes, Lecture notes in mathematics, vol 242, Springer-Verlag, Berlin, Heidelberg, New York (1971). Zbl0224.43006
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  5. [5] A. H. DOOLEY and G. I. GAUDRY, An extension of De Leeuw's theorem to the n-dimensional rotation group, Ann. Inst. Fourier, Grenoble, 34-2 (1984), 111-135. Zbl0523.43002MR86a:43002
  6. [6] A. H. DOOLEY and G. I. GAUDRY, On Lp multipliers of Cartan motion groups, Journal of Functional Analysis, To appear Zbl0597.43005
  7. [7] A. H. DOOLEY and J. W. RICE, On contractions of semisimple Lie groups, Trans Amer. Math. Soc., (1985), 185-202. Zbl0546.22017MR86g:22019
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  10. [10] C. S. HERZ, Une généralisation de la notion de transformée de Fourier-Stieljes, Ann. Inst. Fourier, Grenoble, 24-3 (1974), 145-157. Zbl0287.43006MR54 #13466
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  12. [12] E. HEWITT and K. A. ROSS, Abstract Harmonic Analysis, Vol. I, Springer-Verlag Berlin, Heidelberg, New York (1963). Zbl0115.10603
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  15. [15] R. L. RUBIN, Harmonic analysis on the group of rigid motions of the euclidean plane, Studia Math., 57 (1978), 125-141. Zbl0394.43008MR58 #2030
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  18. [18] N. J. WEISS, A multiplier theorem for SU(n), Proc. Amer. Math. Soc., 59 (1976), 366-370. Zbl0298.22012MR54 #8156

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