Author:
Mandel Rainer,Oliveira e Silva Diogo
Abstract
AbstractWe prove new Fourier restriction estimates to the unit sphere $${\mathbb{S}^{d-1}}$$
S
d
−
1
on the class of O(d − k) × O(k)-symmetric functions, for every d ≥ 4 and 2 ≤ k ≤ d − 2. As an application, we establish the existence of maximizers for the endpoint Stein–Tomas inequality within that class. Moreover, we construct examples showing that the range of Lebesgue exponents in our estimates is sharp.
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Analysis
Reference49 articles.
1. S. Axler, P. Bourdon and W. Ramey, Harmonic Function Theory, Springer, New York, 2001.
2. W. Beckner, Pitt’s inequality with sharp convolution estimates, Proc. Amer. Math. Soc. 136 (2008), 62–65.
3. W. Beckner, Pitt’s inequality and the fractional Laplacian: sharp error estimates, Forum Math. 24 (2012), 62–65.
4. P. Bégout and A. Vargas, Mass concentration phenomena for the L2-critical nonlinear Schrödinger equation, Trans. Amer. Math. Soc. 359 (2007), 62–65.
5. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction. Springer, Berlin–New York, 1976.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. The endpoint Stein–Tomas inequality: old and new;São Paulo Journal of Mathematical Sciences;2024-04-22
2. Block-radial symmetry breaking for ground states of biharmonic NLS;Calculus of Variations and Partial Differential Equations;2024-01-28
3. Symmetric Stein–Tomas, and Why Do We Care?;Trends in Mathematics;2024