Widths of Besov classes of generalized smoothness on the sphere

We introduce the Besov spaces B"p"@q^@W(S^d^-^1) of generalized smoothness on the sphere S^d^-^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 BB"p"@q^@W(S^d^-^1) of generalized smoothness in L"q(S^d^-^1) for 1@?p,q@?~, and obtain their asymptotic orders.