On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces

• Main Author: Ashurov, Ravshan
• Format: Article
• Language: English
• Published: Universiti Putra Malaysia Press 2011
• Online Access: http://psasir.upm.edu.my/id/eprint/40412/1/On%20Nonspherical%20Partial%20Sums%20of%20Fourier%20Integrals%20of%20Continuous.pdf; http://psasir.upm.edu.my/id/eprint/40412/; http://www.pertanika.upm.edu.my/Pertanika%20PAPERS/JST%20Vol.%2019%20%28S%29%20Oct.%202011/07%20Pg%2011-14.pdf
• Institution: Universiti Putra Malaysia

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 orders of the N-fold Fourier integrals of continuous finite functions from the Sobolev spaces Wpa(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