Quadrature in Besov spaces on the Euclidean sphere

Let q1 be an integer, denote the unit sphere embedded in the Euclidean space , and μ_q be its Lebesgue surface measure. We establish upper and lower bounds for

where is the unit ball of a suitable Besov space on the sphere. The upper bounds are obtained for choices of x_k and w_k that admit exact quadrature for spherical polynomials of a given degree, and satisfy a certain continuity condition; the lower bounds are obtained for the infimum of the above quantity over all choices of x_k and w_k. Since the upper and lower bounds agree with respect to order, the complexity of quadrature in Besov spaces on the sphere is thereby established.