Growth and integrability of Fourier transforms on Euclidean space
Classical Analysis and ODEs
2013-08-13 v1
Abstract
A fundamental theme in classical Fourier analysis relates smoothness properties of functions to the growth and/or integrability of their Fourier transform. By using a suitable class of multipliers, a rather general inequality controlling the size of Fourier transforms for large and small argument is proved. As consequences, quantitative Riemann-Lebesgue estimates are obtained and an integrability result for the Fourier transform is developed extending ideas used by Titchmarsh in the one dimensional setting.
Keywords
Cite
@article{arxiv.1308.2268,
title = {Growth and integrability of Fourier transforms on Euclidean space},
author = {William O. Bray},
journal= {arXiv preprint arXiv:1308.2268},
year = {2013}
}