| Автор | Izuml, Masako |
| Автор | Izumi, Shin-Ichi |
| Дата выпуска | 1973 |
| dc.description | Carleson has proved that the Fourier series of functions belonging to the class L<sup>2</sup> converge almost everywhere.Improving his method, Hunt proved that the Fourier series of functions belonging to the class L<sup>p</sup> (p > 1) converge almost everywhere. On the other hand, Kolmogoroff proved that there is an integrable function whose Fourier series diverges almost everywhere. We shall generalise Kolmogoroff's Theorem as follows: There is a function belonging to the class L(logL)<sup>p</sup> (p > 0) whose Fourier series diverges almost everywhere. The following problem is still open: whether “almost everywhere” in the last theorem can be replaced by “everywhere” or not. This problem is affirmatively answered for the class L by Kolmogoroff and for the class L(log logL)<sup>p</sup> (0 < p < 1) by Tandori. |
| Формат | application.pdf |
| Издатель | Cambridge University Press |
| Копирайт | Copyright © Australian Mathematical Society 1973 |
| Название | Divergence of Fourier series |
| Тип | research-article |
| DOI | 10.1017/S0004972700042532 |
| Electronic ISSN | 1755-1633 |
| Print ISSN | 0004-9727 |
| Журнал | Bulletin of the Australian Mathematical Society |
| Том | 8 |
| Первая страница | 289 |
| Последняя страница | 304 |
| Аффилиация | Izuml Masako; Australian National University |
| Аффилиация | Izumi Shin-Ichi; Australian National University |
| Выпуск | 2 |
