Extensions of the theorems of Szász and Zygmund on the absolute convergence of Fourier series
We consider the double Fourier series of functions / : T2 —> C, where T2 is the two-dimensional torus. We prove sufficient conditions on the convergence of the double series whose terms are the /3-th power of the absolute value of the Fourier coefficients of the function / in question. These cond...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
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Bolyai Institute, University of Szeged
Szeged
2008
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| Sorozat: | Acta scientiarum mathematicarum
74 No. 1-2 |
| Kulcsszavak: | Matematika, Fourier-sor |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16233 |
| Tartalmi kivonat: | We consider the double Fourier series of functions / : T2 —> C, where T2 is the two-dimensional torus. We prove sufficient conditions on the convergence of the double series whose terms are the /3-th power of the absolute value of the Fourier coefficients of the function / in question. These conditions are given in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivate in case / is an absolutely continuous function. Our results extend the classical theorems of O. Szász and A. Zygmund from single to double Fourier series. |
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| Terjedelem/Fizikai jellemzők: | 191-206 |
| ISSN: | 0001-6969 |