Generalized monotonicity of sequences and functions of bounded p-variation
It is well known that for a non-negative sequence {an}jf=1 the continuity of the sum J^Li an cos nx is equivalent to the convergence of the series an- We prove that for generalized monotone (a n }q = 1 the last condition implies the so-called p-absolute continuity in the sense of L. C. Young and E....
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2016
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| Sorozat: | Acta scientiarum mathematicarum
82 No. 1-2 |
| Kulcsszavak: | P-változó, approximáció, Fourier-sor, O- és x-reláció, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-014-574-4 |
| Online Access: | http://acta.bibl.u-szeged.hu/40280 |
| Tartalmi kivonat: | It is well known that for a non-negative sequence {an}jf=1 the continuity of the sum J^Li an cos nx is equivalent to the convergence of the series an- We prove that for generalized monotone (a n }q = 1 the last condition implies the so-called p-absolute continuity in the sense of L. C. Young and E. R. Love, where 1 < p < oo. In this case we give estimates for the p-variation moduli of continuity and best approximations in terms of Fourier coefficients of a function. As a corollary of the above results some Konyushkov-type theorems on the equivalence of O- and x-relations are established. |
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| Terjedelem/Fizikai jellemzők: | 111-124 |
| ISSN: | 0001-6969 |