Optimal methods for calculating multidimensional hypersingular integrals

The authors suggest a method of lower estimate of calculation error of multidimensional hypersingular integrals by cubature formulas, applying N nodes of a subintegral function. The estimations has been obtained for arbitrary class of the function $\Psi$, integrated in the sense of Hadamard. For the range of function classes the authors have built cubatury formulas, optimal in order and accuracy.