Estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space

We obtain an estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space. It is shown that, under a suitable choice of the sequence of multi-indices, interpolation polynomials converge to the interpolated function and their rate of convergence is of the order of the best approximation of this function. © Nauka/Interperiodica 2007