Optimal cubature formulae for computing many-dimensional integrals of functions in the class $Q_{r,\gamma}(\Omega,1)$

Order optimal cubature formulae are constructed for evaluating integrals of functions in class $Q_{r,\gamma}(\Omega,1)$, where $\Omega=[-1,1]^l$, $l\ge2$. Asymptotically optimal quadrature formulae are constructed for evaluating integrals of functions in $Q_{r,\gamma}(\Omega,1)$ where $\Omega=[-1,1]$.