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Sobolev estimates for the Radon transform of Melrose and Taylor

✍ Scribed by Andrew Comech

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 336 KB
Volume: 51
Category: Article
ISSN: 0010-3640
DOI: 10.1002/(sici)1097-0312(199805)51:5<537::aid-cpa4>3.0.co;2-9

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✦ Synopsis

We derive the regularity properties of the Radon transform of Melrose and Taylor for the scattering on a compact, convex obstacle with a smooth boundary. The result is formulated in terms of the highest order of contact of tangent lines with the boundary of an obstacle. The main ingredients of the proof are the estimates for degenerate oscillatory integral operators and almost orthogonal decompositions.

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