Dimension‐free Fourier restriction inequalities

Abstract Let denote the best constant for the Fourier restriction inequality to the unit sphere , and let denote the corresponding constant for radial functions. We investigate the asymptotic behavior of the operator norms and as the dimension tends to infinity. We further establish a dimension‐free endpoint Stein–Tomas inequality for radial functions, together with the corresponding estimate for general functions which we prove with an dependence. Our methods rely on a uniform two‐sided refinement of Stempak's asymptotic estimate of Bessel functions.