Order of magnitude of multiple Fourier coefficients of functions of bounded p-variation having lacunary Fourier series
For a Lebesgue integrable complex-valued function / defined over the m-dimensional torus Tm := [0,27r)m, let /(n) denote the Fourier coefficient of/, where n = (n(1) ,... ,n(m)) 6 Zm. Recently, in [Acta Math. Hungar., 128 (2010), 328-343], we have defined the notion of bounded p-variation (p > 1)...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2012
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| Sorozat: | Acta scientiarum mathematicarum
78 No. 1-2 |
| Kulcsszavak: | Matematika, Fourier-sor |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16421 |
| Tartalmi kivonat: | For a Lebesgue integrable complex-valued function / defined over the m-dimensional torus Tm := [0,27r)m, let /(n) denote the Fourier coefficient of/, where n = (n(1) ,... ,n(m)) 6 Zm. Recently, in [Acta Math. Hungar., 128 (2010), 328-343], we have defined the notion of bounded p-variation (p > 1) for a complex-valued function on a rectangle [ai, bi] x • • • x [am. bm] and studied the order of magnitude of Fourier coefficients of such functions on [0, 27r]m. In this paper, the order of magnitude of Fourier coefficients of a function of bounded p-variation (p > 1) from [0, 2tt] rn to C and having lacunary Fourier series with certain gaps is studied and a result analogous to Theorem 2 in [Acta Math. Hungar., 104 (2004), 95-104] and Theorem 2 in [Acta Math. Hungar., 128 (2010), 328-343] is proved. |
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| Terjedelem/Fizikai jellemzők: | 97-109 |
| ISSN: | 0001-6969 |