Some new two-sided inequalities concerning the fourier transform

The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a two-sided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253).

Авторы
Kopezhanova A.1, 2 , Nursultanov E.3 , Persson L.-E. 1, 4, 5
Издательство
Element D.O.O.
Номер выпуска
3
Язык
Английский
Страницы
855-864
Статус
Опубликовано
Том
20
Год
2017
Организации
  • 1 Department of Engineering Sciences and Mathematics Lulea, University of Technology, Lulea, SE 97187, Sweden
  • 2 Faculty of Mechanics and Mathematics L. N. Gumilyov, Eurasian National University, Satpayev st. 2, Astana, 010008, Kazakhstan
  • 3 Kazakhstan Branch of Lomonosov, Moscow State University, Kazhymukan st., 11, Astana, 010010, Kazakhstan
  • 4 UiT, Artic University of Norway, P. O. Box 385, Narvik, Norway
  • 5 RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
Ключевые слова
Fourier transform; Hardy-Littlewood-Stein inequality; Hausdorff-Young's inequality; Inequalities; Lorentz spaces; Network spaces; Total variation; Two-sided estimates
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5461/