Abstract
Salem type conditions for trigonometric series are extended to functions from the Wiener algebra. While in the earlier one-dimensional generalization the conditions are given in terms of the Hilbert transform, for the multivariate setting all reasonable singular integrals are equally involved.
| Original language | English |
|---|---|
| Title of host publication | Operator Theory |
| Subtitle of host publication | Advances and Applications |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 329-339 |
| Number of pages | 11 |
| DOIs | |
| State | Published - 2021 |
Publication series
| Name | Operator Theory: Advances and Applications |
|---|---|
| Volume | 286 |
| ISSN (Print) | 0255-0156 |
| ISSN (Electronic) | 2296-4878 |
Bibliographical note
Publisher Copyright:© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Funding
In November, 2019, the author took part in the conference “New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative”, at Chapman University in Orange, CA, USA. This work is a natural multidimensional extension of the author’s onedimensional study presented as a conference talk. It was inspired largely to the stimulating effect of the meeting and numerous discussions with participants. The author greatly appreciates the efforts of the organizers to create such an atmosphere. The author also thanks the referee for valuable suggestions.
| Funders | Funder number |
|---|---|
| Chapman University |
Keywords
- Fourier transform
- Hardy space
- Hilbert transform
- Riesz transform
- Singular integral
- Wiener algebra