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Sobolev Estimates for Fractional and Singular Radon Transforms

✍ Scribed by Scipio Cuccagna

Book ID: 102972296
Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 936 KB
Volume: 139
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1996.0080

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✦ Synopsis

We prove Sobolev inequalities for singular and fractional Radon transforms which are defined as in a paper of Phong and Stein under certain hypothesis on the corresponding Lagrangian ((N*C)$) which does not necessarily have to be a canonical graph. In the proof we use oscillatory integrals, the Cotlar Stein almost orthogonality theorem, a sort of Littlewood Paley decomposition for a certain operator, some basic facts about Fourier integral operators and pseudodifferential operators. The main ideas come from papers by Phong and Stein (

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