Paraproduct on the Heisenberg group and applications.

Hajer Bahouri; Isabelle Gallagher

Revista Matemática Iberoamericana (2001)

  • Volume: 17, Issue: 1, page 69-105
  • ISSN: 0213-2230

Abstract

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We adapt the homogeneous Littlewood-Paley decomposition on the Heisenberg group constructed by H. Bahouri, P. Gérard et C.-J. Xu in [4] to the inhomogeneous case, which enables us to build paraproduct operators, similar to those defined by J.-M. Bony in [5]; although there is no simple formula for the Fourier transform of the product of two functions, some spectral localization properties of the classical case are preserved on the Heisenberg group after the product has been taken. Using the dyadic decomposition and the paraproduct algorithm, we prove the Gagliardo-Nierenberg inequality on the Heisenberg group; the smoothness of solutions of subelliptic, semi-linear systems is also studied, as well as semi-linear wave equations.

How to cite

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Bahouri, Hajer, and Gallagher, Isabelle. "Paraproduit sur le groupe de Heisenberg et applications.." Revista Matemática Iberoamericana 17.1 (2001): 69-105. <http://eudml.org/doc/39623>.

@article{Bahouri2001,
author = {Bahouri, Hajer, Gallagher, Isabelle},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones de Navier-Stokes; Ecuaciones diferenciales no lineales; Funciones de Littlewood-Paley; Fourier transformation on noncommutative groups; paraproduct; Heisenberg group; irreducible unitary representations; Littlewood-Paley decomposition; sub-elliptic semilinear systems; semilinear wave equations},
language = {fre},
number = {1},
pages = {69-105},
title = {Paraproduit sur le groupe de Heisenberg et applications.},
url = {http://eudml.org/doc/39623},
volume = {17},
year = {2001},
}

TY - JOUR
AU - Bahouri, Hajer
AU - Gallagher, Isabelle
TI - Paraproduit sur le groupe de Heisenberg et applications.
JO - Revista Matemática Iberoamericana
PY - 2001
VL - 17
IS - 1
SP - 69
EP - 105
LA - fre
KW - Ecuaciones de Navier-Stokes; Ecuaciones diferenciales no lineales; Funciones de Littlewood-Paley; Fourier transformation on noncommutative groups; paraproduct; Heisenberg group; irreducible unitary representations; Littlewood-Paley decomposition; sub-elliptic semilinear systems; semilinear wave equations
UR - http://eudml.org/doc/39623
ER -

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