Real Hardy Space, Multidimensional Variations, and Integrability of the Fourier Transform

L. Angeloni, E. Liflyand, G. Vinti

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A new class of functions is introduced closely related to that of functions with bounded Tonelli variation and to the real Hardy space. For this class, conditions for integrability of the Fourier transform are established.

Original languageEnglish
Article number64
JournalComplex Analysis and Operator Theory
Volume14
Issue number6
DOIs
StatePublished - 1 Sep 2020

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Funding

The first and the third author are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilitá e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and they are partially supported by the “Department of Mathematics and Computer Science” of the University of Perugia (Italy) within the project “Metodi di Teoria dell’Approssimazione, Analisi Reale, Analisi Nonlineare e loro applicazioni”. The first and the third author are members of the Gruppo Nazionale per l?Analisi Matematica, la Probabilit? e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and they are partially supported by the ?Department of Mathematics and Computer Science? of the University of Perugia (Italy) within the project ?Metodi di Teoria dell?Approssimazione, Analisi Reale, Analisi Nonlineare e loro applicazioni?.

FundersFunder number
Department of Mathematics and Computer Science?
Department of Mathematics and Computer Science” of the University of Perugia
GNAMPA
Istituto Nazionale di Alta Matematica "Francesco Severi"
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Università degli Studi di Perugia

    Keywords

    • Absolute continuity
    • Bounded variation
    • Fourier transform
    • Hardy space
    • Hilbert transform
    • Riesz transform
    • Tonelli variation

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