A scale of spaces of functions with integrable Fourier transform

Elijah Liflyand

doi:10.1007/s13324-025-01062-w

A scale of spaces of functions with integrable Fourier transform

Elijah Liflyand

Department of Mathematics

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

Abstract

The spaces introduced by Sweezy are, in many respects, natural extensions of the real Hardy space H1(Rd). They are nested in full between H1(Rd) and L01(Rd). Contrary to H1(Rd), they are subject only to atomic characterization. In this paper, the possibilities that atomic expansions allow one are used for proving analogs of the Fourier–Hardy inequality for the Sweezy spaces. The results obtained are used, in dimension one, for extending the scale of the spaces of functions with integrable Fourier transform. An application to trigonometric series is also given.

Original language	English
Article number	63
Journal	Analysis and Mathematical Physics
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/s13324-025-01062-w
State	Published - Jun 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

Keywords

Atomic decomposition
Fourier–Hardy inequality
Integrability of the Fourier transform
Real Hardy space
Sweezy spaces
Trigonometric series

Access to Document

10.1007/s13324-025-01062-w

Cite this

@article{98776a2a3b234d6aa956b0df157445a8,

title = "A scale of spaces of functions with integrable Fourier transform",

abstract = "The spaces introduced by Sweezy are, in many respects, natural extensions of the real Hardy space H1(Rd). They are nested in full between H1(Rd) and L01(Rd). Contrary to H1(Rd), they are subject only to atomic characterization. In this paper, the possibilities that atomic expansions allow one are used for proving analogs of the Fourier–Hardy inequality for the Sweezy spaces. The results obtained are used, in dimension one, for extending the scale of the spaces of functions with integrable Fourier transform. An application to trigonometric series is also given.",

keywords = "Atomic decomposition, Fourier–Hardy inequality, Integrability of the Fourier transform, Real Hardy space, Sweezy spaces, Trigonometric series",

author = "Elijah Liflyand",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.",

year = "2025",

month = jun,

doi = "10.1007/s13324-025-01062-w",

language = "אנגלית",

volume = "15",

journal = "Analysis and Mathematical Physics",

issn = "1664-2368",

publisher = "Springer Science + Business Media",

number = "3",

}

TY - JOUR

T1 - A scale of spaces of functions with integrable Fourier transform

AU - Liflyand, Elijah

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

PY - 2025/6

Y1 - 2025/6

N2 - The spaces introduced by Sweezy are, in many respects, natural extensions of the real Hardy space H1(Rd). They are nested in full between H1(Rd) and L01(Rd). Contrary to H1(Rd), they are subject only to atomic characterization. In this paper, the possibilities that atomic expansions allow one are used for proving analogs of the Fourier–Hardy inequality for the Sweezy spaces. The results obtained are used, in dimension one, for extending the scale of the spaces of functions with integrable Fourier transform. An application to trigonometric series is also given.

AB - The spaces introduced by Sweezy are, in many respects, natural extensions of the real Hardy space H1(Rd). They are nested in full between H1(Rd) and L01(Rd). Contrary to H1(Rd), they are subject only to atomic characterization. In this paper, the possibilities that atomic expansions allow one are used for proving analogs of the Fourier–Hardy inequality for the Sweezy spaces. The results obtained are used, in dimension one, for extending the scale of the spaces of functions with integrable Fourier transform. An application to trigonometric series is also given.

KW - Atomic decomposition

KW - Fourier–Hardy inequality

KW - Integrability of the Fourier transform

KW - Real Hardy space

KW - Sweezy spaces

KW - Trigonometric series

UR - http://www.scopus.com/inward/record.url?scp=105003685265&partnerID=8YFLogxK

U2 - 10.1007/s13324-025-01062-w

DO - 10.1007/s13324-025-01062-w

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:105003685265

SN - 1664-2368

VL - 15

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

IS - 3

M1 - 63

ER -

A scale of spaces of functions with integrable Fourier transform

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this