Mathematical Research Letters

Volume 18 (2011)

Number 4

Extensions of the Stein–Tomas Theorem

Pages: 767 – 781

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n4.a14

Authors

Jong-Guk Bak (Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea)

Andreas Seeger (and Department of Mathematics, University of Wisconsin, Madison, Madison, WI 53706, USA)

Abstract

We prove an endpoint version of the Stein–Tomas restriction theorem, for a general class of measures, and with a strengthened Lorentz space estimate. A similar improvement is obtained for Stein’s estimate on oscillatory integrals of Carleson–Sjölin–Hörmander type and some spectral projection operators on compact manifolds, and for classes of oscillatory integral operators with one-sided fold singularities.

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