Abstract
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights allows one to extend the range of application of such results to Fourier multipliers with unbounded derivatives.
| Original language | English |
|---|---|
| Pages (from-to) | 163-176 |
| Number of pages | 14 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 456 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Dec 2017 |
Bibliographical note
Publisher Copyright:© 2017 Elsevier Inc.
Funding
This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 704030. The first author also acknowledges the support of the Gelbart Institute at the Department of Mathematics of Bar-Ilan University.
| Funders | Funder number |
|---|---|
| Gelbart Institute at the Department of Mathematics of Bar-Ilan University | |
| Horizon 2020 Framework Programme | |
| H2020 Marie Skłodowska-Curie Actions | 704030 |
| Horizon 2020 |
Keywords
- Absolute convergence
- Besov spaces
- Fourier integral
- Gagliardo–Nirenberg inequality
- Weight