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Multiplicateurs de Mikhlin pour une classe particulière de groupes non-unimodulaires

Sami Mustapha (1998)

Annales de l'institut Fourier

On montre, pour une classe particulière de groupes non-unimodulaires G = N , où N est un groupe de Lie stratifié et où l’action de est définie par les dilatations naturelles de N , et pour les sous-laplaciens invariants à gauche correspondants Δ , que toute fonction m H 2 + ϵ ( ) possédant un support compact dans + définit un opérateur m ( Δ ) borné sur les espaces de Lebesgue L p ( G , d r g ) associés à la mesure de Haar invariante à droite sur G , 1 p .

Multiplier theorem on generalized Heisenberg groups II

Waldemar Hebisch, Jacek Zienkiewicz (1996)

Colloquium Mathematicae

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.

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