Widths of Besov classes of generalized smoothness on the sphere

We introduce the Besov spaces BpθΩ(Sd−1) of generalized smoothness on the sphere Sd−1Sd−1, and obtain the representation theorem, an embedding theorem, and the characterization using a frame. We also study the Kolmogorov, linear and Gelfand widths of Besov classes BBpθΩ(Sd−1) of generalized smoothness in Lq(Sd−1)Lq(Sd−1) for 1≤p,q≤∞1≤p,q≤∞, and obtain their asymptotic orders.