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.

Authors
Dyachenko M.1 , Nursultanov E. 2, 3 , Tikhonov S.4, 5, 6
Journal
Journal of Mathematical Analysis and Applications
Publisher
Academic Press Inc.
Number of issue
1
Language
English
Pages
171-184
Status
Published
Link
External link
DOI
10.1016/j.jmaa.2018.06.072
Volume
467
Year
2018
Organizations
  • 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
Keywords
Fourier coefficients/transforms; Hardy and Hardy–Cesàro averages; Hardy–Littlewood theorem; Hausdorff–Young–Paley inequality
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6397/
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