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

The spaces introduced by Sweezy are, in many respects, natural extensions of the real Hardy space H 1 ( R d ) . They are nested in full between H 1 ( R d ) and L 0 1 ( R d ) . Contrary to H 1 ( R d ) , they are subject only to atomic characterization. In this paper, the possibilities that atomic exp...

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Bibliographic Details
Published inAnalysis and mathematical physics Vol. 15; no. 3
Main Author Liflyand, Elijah
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2025
Subjects
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Sweezy spaces
Primary 42B10
42B35
42A32
Integrability of the Fourier transform
Fourier–Hardy inequality
Real Hardy space
Secondary 47B38
42A38
Trigonometric series
Atomic decomposition
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ISSN1664-2368
1664-235X
DOI10.1007/s13324-025-01062-w

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Summary:The spaces introduced by Sweezy are, in many respects, natural extensions of the real Hardy space H 1 ( R d ) . They are nested in full between H 1 ( R d ) and L 0 1 ( R d ) . Contrary to H 1 ( R d ) , 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.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-025-01062-w