Characterization of Sobolev spaces on the sphere

J. A. Barceló, T. Luque, S. Pérez-Esteva

We prove a characterization of the Sobolev spaces $H^{\alpha }$ on the unit sphere ${\mathbb{S}}^{d-1}$, where the smoothness index $\alpha$ is any positive real number and $d\ge 2$. This charac…