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

Galia Dafni; Elijah Liflyand

doi:10.1007/s40627-019-0036-2

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

Galia Dafni, Elijah Liflyand

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Article number	10
Journal	Complex Analysis and its Synergies
Volume	5
Issue number	1
DOIs	https://doi.org/10.1007/s40627-019-0036-2
State	Published - Mar 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Funding

G.D. was partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Centre de recherches mathématiques (CRM) and the Fonds de recherche du Québec—Nature et technologies (FRQNT).

Funders	Funder number
Natural Sciences and Engineering Research Council of Canada
Fonds de recherche du Québec – Nature et technologies

Keywords

Atomic decomposition
Hardy space
Hardy’s inequality
Molecules

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10.1007/s40627-019-0036-2

Cite this

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

Abstract

Bibliographical note

Funding

Keywords

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