Optimal quadrature for weighted function spaces on multivariate domains

Jiansong Li, Heping Wang

Consider the numerical integration $${\mathrm{Int}}_{{\mathbb{S}}^d,w}(f)={\int }_{{\mathbb{S}}^d}f(\mathbf{x})w(\mathbf{x})\mathrm{d}\ddot{I}ƒ(\mathbf{x})$$ for weighted Sobolev classes $B{W}_{p,w}^r({\mathbb{S}}^d)$…