Functions Preserving General Monotone Sequences

Torres-Latorre, Damià

doi:10.1007/s10476-021-0073-y

Anal Math

2021

DOI: 10.1007/s10476-021-0073-y

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Functions Preserving General Monotone Sequences

Damià Torres-Latorre

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Cited by 2 publications

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Functions with general monotone Fourier coefficients

Белов¹,

Dyachenko²,

Tikhonov³

2021

Russ. Math. Surv.

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This paper is a study of trigonometric series with general monotone coefficients in the class with . Sharp estimates are proved for the Fourier coefficients of integrable and continuous functions. Also obtained are optimal results in terms of coefficients for various types of convergence of Fourier series. For

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Functions with general monotone Fourier coefficients

Белов¹,

Dyachenko²,

Tikhonov³

2021

Russ. Math. Surv.

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Функции С Обобщенно Монотонными Коэффициентами Фурье

Белов¹,

Дьяченко²,

Dyachenko

et al. 2021

Uspekhi Mat. Nauk

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В работе исследуются тригонометрические ряды с обобщенно монотонными коэффициентами из класса $\operatorname{GM}(p)$ при $p\geqslant 1$. Получены точные оценки коэффициентов Фурье интегрируемых и непрерывных функций. Доказаны неулучшаемые в своих терминах результаты о различных видах сходимости рядов Фурье. Для $1<p<\infty$ получены двусторонние оценки $L_p$-модулей гладкости сумм рядов с коэффициентами из класса $\operatorname{GM}(p)$, а также (квази-)норм этих сумм в пространствах Лебега, Лоренца, Бесова и Соболева в терминах коэффициентов Фурье. Библиография: 99 названий.

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Functions Preserving General Monotone Sequences

Cited by 2 publications

References 20 publications

Functions with general monotone Fourier coefficients

Functions with general monotone Fourier coefficients

Функции С Обобщенно Монотонными Коэффициентами Фурье

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