On Nonspherical Partial Sums of Fourier Integrals of Continuous Functions from the Sobolev Spaces

The partial integrals of the n-fold fourier integrals connected with elliptic polynomials (not necessarily homogeneous; principal part of which has a strictly convex level surface) are considered. it is proved that if a + s > (n – 1)/2 and ap = n then the riesz means of the nonnegative order s of the n-fold fourier integrals of continuous finite functions from the sobolev spaces wp a(rn) converge uniformly on every compact set, and if a + s > (n – 1)/2 and ap = n, then for any x0 ∈ rn there exists a continuous finite function from the sobolev space such, that the corresponding riesz means of the n-fold fourier integrals diverge to infinity at x0. ams 2000 mathematics subject classifications: primary 42b08; secondary 42c14