Spectral multipliers and multiple-parameter structures on the Heisenberg group

Elias M. Stein

Journées équations aux dérivées partielles (1995)

  • Volume: 1995, page 1-15
  • ISSN: 0752-0360

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Stein, Elias M.. "Spectral multipliers and multiple-parameter structures on the Heisenberg group." Journées équations aux dérivées partielles 1995 (1995): 1-15. <http://eudml.org/doc/93301>.

@article{Stein1995,
author = {Stein, Elias M.},
journal = {Journées équations aux dérivées partielles},
keywords = {spectral multipliers; Marcinkiewicz multiplier; Heisenberg-like groups},
language = {eng},
pages = {1-15},
publisher = {Ecole polytechnique},
title = {Spectral multipliers and multiple-parameter structures on the Heisenberg group},
url = {http://eudml.org/doc/93301},
volume = {1995},
year = {1995},
}

TY - JOUR
AU - Stein, Elias M.
TI - Spectral multipliers and multiple-parameter structures on the Heisenberg group
JO - Journées équations aux dérivées partielles
PY - 1995
PB - Ecole polytechnique
VL - 1995
SP - 1
EP - 15
LA - eng
KW - spectral multipliers; Marcinkiewicz multiplier; Heisenberg-like groups
UR - http://eudml.org/doc/93301
ER -

References

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  1. [C] Christ, M., Lp bounds for spectral multipliers on nilpotent groups, Trans. Amer. Math. Soc., 328, (1991), 73-81. Zbl0739.42010MR92k:42017
  2. [CW] Coifman, R. and Weiss, G., Transference methods in analysis, CBMS Survey, # 31, (1977). Zbl0377.43001MR58 #2019
  3. [CZ] Calderón, A. and Zygmund, A., On the existence of certain singular integrals, Acta Math., 88, (1952), 85-139. Zbl0047.10201MR14,637f
  4. [FS] Fefferman, R. and Stein, E., Singular integrals on product spaces, Adv. in Math., 45, (1982), 117-143. Zbl0517.42024MR84d:42023
  5. [G] Geller, D., Fourier analysis on the Heisenberg group, Proc. Nat. Acad. Sci., 74, (1977), 1328-1331. Zbl0351.43012MR58 #6069
  6. [H] Hörmander, L., Estimates for translation-invariant operators on Lp spaces, Acta Math., 104, (1960), 93-139. Zbl0093.11402
  7. [He] Hebisch, W., Multiplier theorems on generalized Heisenberg groups, Colloq. Math., 65, (1993), 231-239. Zbl0841.43009MR94m:43013
  8. [Ma] Marcinkiewicz, J., Sur les multiplicateurs des séries de Fourier, Studia Math., 8, (1939), 78-91. Zbl0020.35403MR1,329aJFM65.0257.02
  9. [Mi] Mihlin, S.G., On the multipliers of Fourier integrals, Dok. Akact. Nouk, 109, (1956), 701-703. Zbl0073.08402MR18,304a
  10. [MS] Müller, D. and Stein, E., On spectral multipliers for Heisenberg and related groups, J. Math. Pures Appl., 73, (1994), 413-440. Zbl0838.43011MR96m:43004
  11. [MRS1] Müller, D., Ricci, F. and Stein, E., Marcinkiewicz multipliers and multiparameter structure on Heisenberg (-type) group, I, Invent. Math., 119, (1995), 199-233. Zbl0857.43012
  12. [MRS2] Müller, D., Ricci, F. and Stein, E., Marcinkiewicz multipliers and multiparameter structure on Heisenberg (-type) group, II, Math. Zeitschrift, (to appear). Zbl0863.43001
  13. [P] Peetre, J., The Weyl transform and Laguerre polynomials, Le Math. (Catania), 27, (1972), 301-323. Zbl0276.44005MR49 #5426
  14. [PS] Phong, D.H. and Stein, E., Some further classes of pseudo-differential and singular integral operators arising in boundary-value problems, Amer. Jour. Math., 104, (1982), 141-172. Zbl0526.35079MR84j:35163
  15. [S] Stein, E., Singular integrals and differentiability properties of functions, Princeton University Press, 1970. Zbl0207.13501MR44 #7280

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