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Sobolev estimates for the Radon transform of Melrose and Taylor
Article first published online: 6 DEC 1998
DOI: 10.1002/(SICI)1097-0312(199805)51:5<537::AID-CPA4>3.0.CO;2-9
Copyright © 1998 John Wiley & Sons, Inc.
1097-0312/asset/cover.gif?v=1&s=27e2b2132052ff78aa82eddfab7608281350adb9 "Communications on Pure and Applied Mathematics")
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How to Cite
Comech, A. (1998), Sobolev estimates for the Radon transform of Melrose and Taylor. Comm. Pure Appl. Math., 51: 537–550. doi: 10.1002/(SICI)1097-0312(199805)51:5<537::AID-CPA4>3.0.CO;2-9
Publication History
- Issue published online: 6 DEC 1998
- Article first published online: 6 DEC 1998
- Manuscript Received: JAN 1997
- Abstract
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Abstract
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. © 1998 John Wiley & Sons, Inc.