Precise Estimates for Weight Functions Satisfying a Weighted Fourier Transform Inequality

Abstract

This paper shows that for a given weighted Fourier transform inequality, certain weight functions will satisfy it. The work done in my paper is a continuation of similar ideas found in Yuki Yayama's thesis. She proved that a nonessentially increasing weight function w with a finite number of zeros can satisfy a given weighted Fourier transform inequality. Her proof includes estimations of distribution functions, the sine and the arcsine functions both near zero. My paper provides another proof by using precise values of distribution functions certain approximations used only when necessary.