A MULTIDIMENSIONAL ANALOG OF A THEOREM OF WHITNEY

The following theorem is proved:Theorem. Let , where is a convex domain in . Then where the on the left is taken over all degree polynomials, and the norm on the right is taken over the set in which the th difference is defined. The constant depends only on , , and the ratio of the diameter of to its width.H. Whitney proved this theorem in the case and . As a corollary, it is proved that the -modulus of continuity dominates any "deviation", constructed with the help of a measure with compact support, orthogonal to polynomials of degree .Bibliography: 10 items.