Dispersive estimates for principally normal pseudodifferential operators
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- 2 November 2004
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 58 (2) , 217-284
- https://doi.org/10.1002/cpa.20067
Abstract
In this article we construct parametrices and obtain dispersive estimates for a large class of principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used to prove Lq Carleman inequalities, which in turn yield unique continuation results for various partial differential operators with rough potentials.Keywords
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This publication has 21 references indexed in Scilit:
- ON THE FEFFERMAN–PHONG INEQUALITY AND RELATED PROBLEMSCommunications in Partial Differential Equations, 2002
- STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTSCommunications in Partial Differential Equations, 2002
- Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficientsCommunications on Pure and Applied Mathematics, 2001
- Carleman inequalities and the heat operatorDuke Mathematical Journal, 2000
- A parametrix construction for wave equations with $C^{1,1}$ coefficientsAnnales de l'institut Fourier, 1998
- Carleman Type Estimates in an Anisotropic Case and ApplicationsJournal of Differential Equations, 1993
- A property of measures inR N and an application to unique continuationGeometric and Functional Analysis, 1992
- Norm estimates in besov and Lizorkin-Triebel spaces for the solutions of second-order linear hyperbolic equationsJournal of Mathematical Sciences, 1991
- Strong Uniqueness Theorems for Second Order Elliptic Differential EquationsAmerican Journal of Mathematics, 1990
- Differential operators of principal typeMathematische Annalen, 1960