Order estimates for Lebesgue constants of Fourier sums in Orlicz spaces
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Order estimates for Lebesgue constants of Fourier sums in Orlicz spaces
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| Автор |
Yur’evich, Antonov, N.
Lukoyanov, A. N. |
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| Тематика |
FOURIER SERIES
LEBESGUE CONSTANTS ORLICZ SPACE |
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| Описание |
We consider the problem of order estimates for partial sums of trigonometric Fourier series as operators from Orlicz spaces Lϕ2π to the space of 2π-periodic continuous functions C2π. It is established that an arbitrary function ϕ generating an Orlicz class satisfies the estimate
Sn(f) C2π ≤ Cϕ−1(n) ln(n + 1) f Lϕ 2π, (∗) where f ∈ Lϕ2π, n ∈ N, Sn(f) is the nth partial sum of the trigonometric Fourier series of f, and the constant C > 0 is independent of f and n. In addition, it is shown that if the function ϕ satisfies the ∆2-condition, then the estimate can be improved. More exactly, Sn(f) C2π ≤ Cϕ−1(n) f Lϕ 2π, f ∈ Lϕ2π, n ∈ N, C = C(ϕ). (∗∗) Counterexamples are constructed, which show that if ϕ satisfies the ∆2-condition, then estimate (∗∗) is unimprovable in order on the space Lϕ2π and, if ϕ satisfies the ∆2-condition, then estimate (∗) is unimprovable in order on the space Lϕ2π © 2021 The authors. |
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| Дата |
2024-04-08T11:07:50Z
2024-04-08T11:07:50Z 2022 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Антонов, НЮ & Лукоянов, АН 2021, 'Порядковые оценки констант Лебега сумм Фурье в пространствах Орлича', Труды института математики и механики УрО РАН, Том. 27, № 4, стр. 35-47. https://doi.org/10.21538/0134-4889-2021-27-4-35-47
Антонов, Н. Ю., & Лукоянов, А. Н. (2021). Порядковые оценки констант Лебега сумм Фурье в пространствах Орлича. Труды института математики и механики УрО РАН, 27(4), 35-47. https://doi.org/10.21538/0134-4889-2021-27-4-35-47 0134-4889 Final All Open Access; Bronze Open Access http://journal.imm.uran.ru/sites/default/files/content/27_4/TrIMMUrORAN_2021_4_p35_L.pdf http://journal.imm.uran.ru/sites/default/files/content/27_4/TrIMMUrORAN_2021_4_p35_L.pdf http://elar.urfu.ru/handle/10995/131521 47228414 10.21538/0134-4889-2021-27-4-35-47 85142193835 000756004700003 |
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| Язык |
ru
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Krasovskii Institute of Mathematics and Mechanics
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| Источник |
Trudy Instituta Matematiki i Mekhaniki UrO RAN
Trudy Instituta Matematiki i Mekhaniki UrO RAN |
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