On weighted conditions for the absolute convergence of Fourier integrals
arXiv:1811.07326 · doi:10.1016/j.jmaa.2017.06.083
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.