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arXiv · 1811.07326

On weighted conditions for the absolute convergence of Fourier integrals

Yu. Kolomoitsev·E. Liflyand
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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.

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Yu. Kolomoitsev, E. Liflyand. 2018-11-18. On weighted conditions for the absolute convergence of Fourier integrals. https://doi.org/10.1016/j.jmaa.2017.06.083

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