Weak coupling limit for Schr\"odinger operators with degenerate kinetic energy for a large class of potentials

We improve results by Frank et al. [11] and Hainzl-Seiringer [19] on the weak coupling limit of eigenvalues for Schr\"odinger operators whose kinetic energy vanishes on a codimension one submanifold. The main technical innovation that allows us to go beyond the potentials considered in [11, 19] is the use of the Tomas-Stein theorem.