A local Hilbert transform, Hardy’s inequality and molecular characterization of Goldberg’s local Hardy space

We prove characterizations of Goldberg’s local Hardy space h1(R) by means of a local Hilbert transform and a molecular decomposition. We use this decomposition to prove a version of Hardy’s inequality for the Fourier transform of functions in this space. © 2019, Springer Nature Switzerland AG.

Authors
Dafni G.1 , Liflyand E. 2, 3
Journal
Complex Analysis and its Synergies
Publisher
Springer International Publishing
Number of issue
1
Language
English
Status
Published
Link
External link
DOI
10.1007/S40627-019-0036-2
Number
10
Volume
5
Year
2019
Organizations
  • 1 Department of Mathematics and Statistics, Concordia University, Montréal, QC, Canada
  • 2 Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel
  • 3 S.M. Nikol’skii Institute of Mathematics, RUDN University, 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
Keywords
Atomic decomposition; Hardy space; Hardy’s inequality; Molecules
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