Herz versus Fefferman

Abstract: We study Bochner--Riesz summability for a one-dimensional model of noncompact manifolds with ends. The central point is the contrast between the symmetric and asymmetric cases. When the end dimensions agree, the model follows Herz's radial theory for the Euclidean Laplacian. When they are unequal, a Fefferman-type obstruction appears, analogous to the ball multiplier obstruction in higher-dimensional Fourier analysis, even though the model itself is one-dimensional.

This is based on joint project with Peng Chen, Dangyang He and Lixin Yan.