Multiplier theorem on generalized Heisenberg groups II

Waldemar Hebisch; Jacek Zienkiewicz

Colloquium Mathematicae (1996)

  • Volume: 69, Issue: 1, page 29-36
  • ISSN: 0010-1354

Abstract

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We prove that on a product of generalized Heisenberg groups, a Hörmander type multiplier theorem for Rockland operators is true with the critical index n/2 + ϵ, ϵ>0, where n is the euclidean (topological) dimension of the group.

How to cite

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Hebisch, Waldemar, and Zienkiewicz, Jacek. "Multiplier theorem on generalized Heisenberg groups II." Colloquium Mathematicae 69.1 (1996): 29-36. <http://eudml.org/doc/210322>.

@article{Hebisch1996,
abstract = {We prove that on a product of generalized Heisenberg groups, a Hörmander type multiplier theorem for Rockland operators is true with the critical index n/2 + ϵ, ϵ>0, where n is the euclidean (topological) dimension of the group.},
author = {Hebisch, Waldemar, Zienkiewicz, Jacek},
journal = {Colloquium Mathematicae},
keywords = {generalized Heisenberg groups; Hörmander type multiplier theorem; Rockland operators},
language = {eng},
number = {1},
pages = {29-36},
title = {Multiplier theorem on generalized Heisenberg groups II},
url = {http://eudml.org/doc/210322},
volume = {69},
year = {1996},
}

TY - JOUR
AU - Hebisch, Waldemar
AU - Zienkiewicz, Jacek
TI - Multiplier theorem on generalized Heisenberg groups II
JO - Colloquium Mathematicae
PY - 1996
VL - 69
IS - 1
SP - 29
EP - 36
AB - We prove that on a product of generalized Heisenberg groups, a Hörmander type multiplier theorem for Rockland operators is true with the critical index n/2 + ϵ, ϵ>0, where n is the euclidean (topological) dimension of the group.
LA - eng
KW - generalized Heisenberg groups; Hörmander type multiplier theorem; Rockland operators
UR - http://eudml.org/doc/210322
ER -

References

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  11. [11] B. Helffer et J. Nourrigat, Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe gradué, Comm. Partial Differential Equations 3 (1978), 889-958. Zbl0423.35040
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  13. [13] A. Hulanicki, The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group, Studia Math. 56 (1976), 165-179. Zbl0336.22007
  14. [14] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators, ibid. 80 (1984), 235-244. 
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  17. [17] J. Randall, The heat kernel for generalized Heisenberg groups, to appear. Zbl0897.43007

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