On the multiple Fourier integrals of continuous functions from the Sobolev spaces
The partial integrals of the TV-fold Fourier integrals connected with elliptic polynomials (with 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 iV-fold Fourier integrals of continuous finit...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2011
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| Sorozat: | Acta scientiarum mathematicarum
77 No. 1-2 |
| Kulcsszavak: | Matematika, Szoboljev-tér, Fourier-sor, Fourier-integrál, Függvény |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16385 |
| Tartalmi kivonat: | The partial integrals of the TV-fold Fourier integrals connected with elliptic polynomials (with 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 iV-fold Fourier integrals of continuous finite functions from the Sobolev spaces W£(RN ) converge uniformly on every compact set, and if a + s = (N — 1)/2, ap = N, then for any XQ £ RN there exists a continuous finite function from the Sobolev space Wp(RN ) such that the corresponding Riesz means of the TV-fold Fourier integrals diverge to infinity at X0. |
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| Terjedelem/Fizikai jellemzők: | 209-222 |
| ISSN: | 0001-6969 |