Remarks on dispersive estimates and curvature

Fabio Nicola

doi:10.3934/cpaa.2007.6.203

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2007, Volume 6, Issue 1: 203-212. Doi: 10.3934/cpaa.2007.6.203

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Remarks on dispersive estimates and curvature

Fabio Nicola^1,

1.
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino

Received: February 28, 2006

Revised: September 30, 2006

Published: February 2007

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Abstract

We investigate connections between certain dispersive estimates of a (pseudo) differential operator of real principal type and the number of non-vanishing curvatures of its characteristic manifold. More precisely, we obtain sharp thresholds for the range of Lebesgue exponents depending on the specific geometry.

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Mathematics Subject Classification: Primary: 35S05; Secondary: 35B45, 47G30.

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