Absolutely convergent double Fourier series and generalized multiplicative Lipschitz classes of functions
We investigate the order of magnitude of the modulus of continuity of a function f(x,y) with absolutely convergent double Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that / belong to one of the generalized Lipschitz classes Lip(a, /3; L) and Lip(a, /3;...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2009
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| Sorozat: | Acta scientiarum mathematicarum
75 No. 3-4 |
| Kulcsszavak: | Matematika, Fourier-sor, Lipschitz-függvényosztályok |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16323 |
| Tartalmi kivonat: | We investigate the order of magnitude of the modulus of continuity of a function f(x,y) with absolutely convergent double Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that / belong to one of the generalized Lipschitz classes Lip(a, /3; L) and Lip(a, /3; 1/L), where 0 < a,/3 < 1, L = L(x,y) = L\(x)L2(y) is positive and L\(x) and L2(y) are non-decreasing, slowly varying functions such that L\(x),L2(y) —» oo as x,y —» oo . These sufficient conditions are also necessary in the case of a certain subclass of Fourier coefficients. |
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| Terjedelem/Fizikai jellemzők: | 617-633 |
| ISSN: | 0001-6969 |