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 language | English |
|---|---|
| Article number | 64 |
| Journal | Complex Analysis and Operator Theory |
| Volume | 14 |
| Issue number | 6 |
| DOIs | |
| State | Published - 1 Sep 2020 |
Bibliographical note
Funding Information: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”.
Funding Information:
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?.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
Keywords
- Absolute continuity
- Bounded variation
- Fourier transform
- Hardy space
- Hilbert transform
- Riesz transform
- Tonelli variation