标题： 关于星形区域上Sobolev函数类的求积公式优化 显示英文标题

标题： On optimization of cubature formulae for Sobolev classes of functions defined on star domains

摘要： 我们找到在给定函数在有限个点的值的情况下，对定义在有界星形区域上的多变量函数类的积分算子的渐近最优恢复方法，这些函数的分布梯度在$L_p$范数下是有界的；因此，我们推广了当函数定义域为凸域时，这一优化问题的已知解。 显示英文摘要

摘要： We find asymptotically optimal methods of recovery of the integration operator given values of the function at a finite number of points for a class of multivariate functions defined on a bounded star domain that have bounded in $L_p$ norm of their distributional gradient; thus we generalize the known solution of this optimization problem in the case, when the domain of definition of the functions is convex.