Hardy–Littlewood and Pitt's inequalities for Hausdorff operators

In this paper we study transformed trigonometric series with Hausdorff averages of Fourier coefficients. We prove Hardy–Littlewood and Pitt's inequalities for such series. The corresponding results for the Hausdorff averages of the Fourier transforms are also obtained. © 2018 Elsevier Masson SAS

Authors
Dyachenko M.1 , Nursultanov E. 2, 3 , Tikhonov S.4, 5, 6
Journal
Bulletin des Sciences Mathematiques
Publisher
Elsevier Masson SAS
Language
English
Pages
40-57
Status
Published
Link
External link
DOI
10.1016/J.BULSCI.2018.06.003
Volume
147
Year
2018
Organizations
  • 1 Lomonosov Moscow State University, Vorobyevy Gory 1, Moscow, 119991, Russian Federation
  • 2 Lomonosov Moscow State University (Kazakhstan Branch), Kazhimukan 11, Astana, 010010, Kazakhstan
  • 3 RUDN University, S.M. Nikolskii Mathematical Institute, Miklukho-Maklay 6, 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; Hardy–Littlewood theorem; Hausdorff operators; Pitt's inequality
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