%0 Journal Article
%T Growth and integrability of Fourier transforms on Euclidean space
%A William O. Bray
%J Mathematics
%D 2013
%I arXiv
%X 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 $L^{p}-$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.
%U http://arxiv.org/abs/1308.2268v1