2026-09-19T13:16:19Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1553212024-06-28T03:37:31Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Guth, Lawrence
Ortiz, Alexander
Massachusetts Institute of Technology. Department of Mathematics
2024-06-27T19:44:49Z
2024-06-27T19:44:49Z
2024-05
2024-05-15T16:20:47.448Z
https://hdl.handle.net/1721.1/155321
In Fourier restriction theory, weighted inequalities allow us to probe the shape of level sets. In this thesis, we describe a new weighted Fourier extension estimate for the cone and its connection with the Mizohata–Takeuchi conjecture. The main result Theorem 3.1 builds on techniques from geometry originally explored by Tom Wolff in this context. The proof uses circular maximal function estimates first proved by Wolff and later generalized by Pramanik–Yang–Zahl in their work on restricted projections as a black box.
Ph.D.
Massachusetts Institute of Technology
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https://creativecommons.org/licenses/by-nc-nd/4.0/
Sparse Fourier restriction for the cone
Thesis
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Doctoral
Doctor of Philosophy
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