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Resolvent estimates related with a class of dispersive equations

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Type
Preprint
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Submission Date
Identifiers
arXiv ID: 0704.0347
Source
arXiv
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Unknown
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Abstract

We present a simple proof of the resolvent estimates of elliptic Fourier multipliers on the Euclidean space, and apply them to the analysis of time-global and spatially-local smoothing estimates of a class of dispersive equations. For this purpose we study in detail the properties of the restriction of Fourier transform on the unit cotangent sphere associated with the symbols of multipliers.

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