Lebesgue inequalities for poisson integrals
We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceL p ,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofL p . We show that the es...
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| Datum: | 2000 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2000
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4474 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We obtain estimates for the deviations of the Fourier partial sums on the sets of the Poisson integrals of functions from the spaceL p ,p≥1, that are expressed in terms of the values of the best approximations of such functions by trigonometric polynomials in the metric ofL p . We show that the estimates obtained are unimprovable on some important functional subsets. |
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