Abstract
In this paper we study the worst-case error of numerical integration on the unit sphere Sd⊂Rd+1, d≥2, for certain spaces of continuous functions on Sd. For the classical Sobolev spaces Hs(Sd) (s>d2) upper and lower bounds for the worst case integration error have been obtained in Brauchart and Hesse (2007), Hesse (2006) and Hesse and Sloan (2005,2006). We investigate the behaviour for s→d2+ by introducing spaces Hd2,γ(Sd), γ>12, with an extra logarithmic weight. For these spaces we obtain similar upper and lower bounds for the worst case integration error.
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