Hardy-type theorems on Fourier transforms revised

We obtain new conditions on periodic integrable functions so that their transformed Fourier series belong to Lp. This improves the classical Hardy and Bellman results. A counterpart for the Fourier transforms is also established. Our main tool is a new extension of the Hausdorff–Young–Paley inequality for Fourier transforms. © 2018 Elsevier Inc.

Авторы
Dyachenko M.1 , Nursultanov E. 2, 3 , Tikhonov S.4, 5, 6
Редакторы
-
Издательство
Academic Press Inc.
Номер выпуска
1
Язык
Английский
Страницы
171-184
Статус
Опубликовано
Подразделение
-
Номер
-
Том
467
Год
2018
Организации
  • 1 Moscow State University, Vorobyevy Gory 1, Moscow, 119991, Russian Federation
  • 2 Lomonosov Moscow State University (Kazakh Branch), Munatpasova 7, Astana, 010010, Kazakhstan
  • 3 RUDN University, S.M. Nikol'skii Mathematical Institute, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
  • 4 Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Bellaterra (Barcelona), 08193, Spain
  • 5 ICREA, Pg. Lluís Companys 23, Barcelona, 08010, Spain
  • 6 Universitat Autònoma de Barcelona, Spain
Ключевые слова
Fourier coefficients/transforms; Hardy and Hardy–Cesàro averages; Hardy–Littlewood theorem; Hausdorff–Young–Paley inequality
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6397/