On weighted conditions for the absolute convergence of Fourier integrals

Yu Kolomoitsev; E. Liflyand

doi:10.1016/j.jmaa.2017.06.083

On weighted conditions for the absolute convergence of Fourier integrals

Yu Kolomoitsev, E. Liflyand

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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	https://doi.org/10.1016/j.jmaa.2017.06.083
State	Published - 1 Dec 2017

Bibliographical note

Funding 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.

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

Absolute convergence
Besov spaces
Fourier integral
Gagliardo–Nirenberg inequality
Weight

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10.1016/j.jmaa.2017.06.083

Cite this

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On weighted conditions for the absolute convergence of Fourier integrals

Abstract

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Keywords

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