Year: 2024
Type: article
Abstract: A well-known conjecture states that constant functions are extremizers of the L^{2} \to L^{6} Tomas–Stein extension inequality for the circle. We prove that functions supported in a \sqrt{6}/80 -neighborhood of a pair of antipodal points on S^{1} satisfy the conjectured sharp inequality. In the process, we make progress on a program formulated by Carneiro, Foschi, Oliveira e Silva and Thiele to prove the sharp inequality for all functions.
DOI: 10.4171/rmi/1532
Author: Lars Becker
Institution: University of Bonn
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404140198