The endpoint Stein–Tomas inequality: old and new

Diogo Oliveira e Silva

Type: Article

Publication Date: 2024-04-22

Citations: 0

DOI: https://doi.org/10.1007/s40863-024-00422-x

Abstract

Abstract The Stein–Tomas inequality from 1975 is a cornerstone of Fourier restriction theory. Despite its respectable age, it is a fertile ground for current research. This note is centered around three classical applications – to Strichartz inequalities, Salem sets and Roth’s theorem in the primes – and three recent improvements: the sharp endpoint Stein–Tomas inequality in three space dimensions, maximal and variational refinements, and the symmetric Stein–Tomas inequality with applications.

Locations

São Paulo Journal of Mathematical Sciences - View - PDF

Similar Works

Action	Title	Year	Authors
+	The Stein–Tomas inequality under the effect of symmetries	2023	Rainer Mandel Diogo Oliveira e Silva
+	The Tomas–Stein inequality under the effect of symmetries	2021	Rainer Mandel Diogo Oliveira e Silva
+	The Stein-Tomas inequality under the effect of symmetries	2021	Diogo Oliveira e Silva Rainer Mandel
+	Correction to: The endpoint Stein–Tomas inequality: old and new	2024	Diogo Oliveira e Silva
+ PDF Chat	On a version of Trudinger–Moser inequality with Möbius shift invariance	2010	Adimurthi Kyril Tintarev
+	Improved Stein inequalities for the Fourier transform	2023	Erlan Nursultanov Durvudkhan Suragan
+	The Stein-Tomas inequality in trace ideals	2016	Rupert L. Frank Julien Sabin
+ PDF Chat	The Stein-Tomas inequality in trace ideals	2016	Rupert L. Frank Julien Sabin
+	A note on maximal Fourier Restriction for spheres in all dimensions	2017	Marco Vitturi
+ PDF Chat	Some Inequalities for the Fourier Transform and Their Limiting Behaviour	2023	Nicola Garofalo
+	Refinements of Kolmogorov’s Inequality	1969	Peter Whittle
+	Refinements of Ostrowski’s and Fan-Todd’s Inequalities	1998	Momčilo Bjelica
+ PDF Chat	The Brascamp–Lieb inequality and its influence on Fourier analysis	2022	Ruixiang Zhang
+	The Brascamp-Lieb inequality and its influence on Fourier analysis	2022	Ruixiang Zhang
+	REFINEMENTS OF CARLEMAN’S INEQUALITY	2014	Yu‐Ming Chu Xiaoming Zhang Xu Qian
+	Salem sets and restriction properties of Fourier transforms	2000	Gerd Mockenhaupt
+	Improved Stein inequalities for the Fourier transform	2024	Erlan Nursultanov Durvudkhan Suragan
+	Sets of Salem type and sharpness of the 𝐿²-Fourier restriction theorem	2015	Xianghong Chen
+ PDF Chat	The Stein-Tomas inequality in trace ideals	2016	Rupert L. Frank Julien Sabin
+	Restriction Theorem for the Fourier–Dunkl Transform and Its Applications to Strichartz Inequalities	2024	P Jitendra Kumar Senapati Pradeep Boggarapu Shyam Swarup Mondal Hatem Mejjaoli

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (29)

Action	Title	Year	Authors
+	Nonlinear Dispersive Equations	2006	Terence Tao
+ PDF Chat	Oscillatory integrals and multiplier problem for the disc	1972	Lennart Carleson Per Sjölin
+	Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators	1987	Carlos E. Kenig Alberto Ruiz Christopher D. Sogge
+	Remarks on Montgomery's conjectures on dirichlet sums	1991	Jean Bourgain
+	Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations	1977	Robert S. Strichartz
+	On Λ(p)-subsets of squares	1989	Jean Bourgain
+	Salem sets and restriction properties of Fourier transforms	2000	Gerd Mockenhaupt
+ PDF Chat	On the Sharpness of Mockenhaupt’s Restriction Theorem	2013	Kyle Hambrook Izabella Łaba
+ PDF Chat	Inequalities for strongly singular convolution operators	1970	Charles Fefferman
+ PDF Chat	A restriction theorem for the Fourier transform	1975	Peter A. Tomas