Sharp estimates for oscillatory integral operators via polynomial partitioning
By Larry Guth, J. Hickman, Marina Iliopoulou. Acta Mathematica, 2017
72 citations recorded by the source corpus.
The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7aa70ff3b1a36d5b054e5f44a5566a84534c70c5
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In Applied Mathematics
- Xiumin Du
- Ruixiang Zhang
- J. Hickman
- Keith McKenzie Rogers
- Hong Wang
- Yumeng Ou
- Larry Guth
- Bobby Wilson
In Mathematical Physics
- Xiumin Du
- Ruixiang Zhang
- J. Hickman
- Keith McKenzie Rogers
- Larry Guth
- Hong Wang
- Yumeng Ou
- Bobby Wilson
Citations in the corpus
- Weighted restriction estimates and application to Falconer distance set problem (2018, background): “It follows from the variable-coefficient generalization as discussed in [10, 11], that the same weighted restriction estimates in Theorem 1.”
- Improved Fourier restriction estimates in higher dimensions (2018, methodology): “urvature. For instance, for the prototypical example of a graph of a non-degenerate quadratic form, the transverse equidistribution estimate from Lemma 8.4 fails to hold in mixed signature cases (see [13] for further discussion of such phenomena). Remark 11.4. Another possible direction in which to ”