Extensions of the Stein-Tomas theorem

By Jong-Guk Bak, Andreas Seeger. 2010

71 citations recorded by the source corpus.

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-Sj\"olin-H\"ormander type and some spectral projection operators on compact manifolds, and for classes of oscillatory integral operators with one-sided fold singularities.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ff8a3af2aeaf7da728957553243d4c49cbd91ad6

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In Applied Mathematics

1. Pablo Shmerkin
2. P. P. Varj'u

In Mathematical Physics

1. Pablo Shmerkin
2. Meng Wu
3. P. P. Varj'u
4. Michael Hochman
5. Jonathan M. Fraser

Citations in the corpus

• Salem sets with no arithmetic progressions (2015, methodology): “δ + δ′ 2 . Thus y ∈ Im,j+k ∩ I(X), but this implies that {2j,j + k,2k} is a non-trivial 3-AP in X, which is impossible by construction. 2.3. Proof of main results. By iterating the set transformation [0,1] → I(X), one can construct a self-similar set of dimension > 1 − ε with no progressions, but”