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).

Authors
Kopezhanova A. 1, 2 , Nursultanov E. 3 , Persson L.-E. 1, 4, 5
Journal
Mathematical Inequalities and Applications
Publisher
Element D.O.O.
Issue number
3
Language
English
Pages
855-864
State
Published
Link
External link
DOI
10.7153/MIA-20-54
Volume
20
Year
2017
Organizations
  • 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
Keywords
Fourier transform; Hardy-Littlewood-Stein inequality; Hausdorff-Young's inequality; Inequalities; Lorentz spaces; Network spaces; Total variation; Two-sided estimates
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