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Vanishing of the first reduced cohomology with values in an $L^{p}$ -representation

Romain Tessera (2009)

Annales de l’institut Fourier

We prove that the first reduced cohomology with values in a mixing $L^{p}$ -representation, $1 < p < \infty$ , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced $ℓ^{p}$ -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced $L^{p}$ -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes. We also...

Displaying 1 – 4 of 4

Vanishing of the first reduced cohomology with values in an $L^{p}$ -representation

Variantes des inégalités de Sobolev et inégalités de Trudinger pour les groupes de Lie et les variétés riemanniennes.

Vector-valued Calderón-Zygmund theory and Carleson measures on spaces of homogeneous nature

Vector-Valued Fourier Multipliers on Symmetric Spaces of the Noncompact Type.

Currently displaying 1 – 4 of 4

Displaying 1 – 4 of 4

Vanishing of the first reduced cohomology with values in an L p -representation

Variantes des inégalités de Sobolev et inégalités de Trudinger pour les groupes de Lie et les variétés riemanniennes.

Vector-valued Calderón-Zygmund theory and Carleson measures on spaces of homogeneous nature

Vector-Valued Fourier Multipliers on Symmetric Spaces of the Noncompact Type.

Currently displaying 1 – 4 of 4

Vanishing of the first reduced cohomology with values in an $L^{p}$ -representation