Citation
Ashurov, Ravshan
(2011)
On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces.
Pertanika Journal of Science & Technology, 19 (S).
pp. 1114.
ISSN 01287680; ESSN: 22318526
Abstract / Synopsis
The partial integrals of the Nfold 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 Nfold 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 Nfold Fourier integrals diverge to infinity at x0. AMS
2000 Mathematics Subject Classifications: Primary 42B08; Secondary 42C14
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