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.
Bibliographical noteFunding Information:
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.
© 2017 Elsevier Inc.
- Absolute convergence
- Besov spaces
- Fourier integral
- Gagliardo–Nirenberg inequality