Improved Stein inequalities for the Fourier transform

Abstract

In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise version of the Stein inequality for the Fourier transform, broadening its applicability from the range $1<p<2$ to $2\le p<\infty$.

15 pages, to appear in Journal of Approximation Theory