On weighted conditions for the absolute convergence of Fourier integrals
Classical Analysis and ODEs
2018-11-20 v1
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.
Keywords
Cite
@article{arxiv.1811.07326,
title = {On weighted conditions for the absolute convergence of Fourier integrals},
author = {Yu. Kolomoitsev and E. Liflyand},
journal= {arXiv preprint arXiv:1811.07326},
year = {2018}
}