The Bedrosian identity for [formula omitted] functions

Abstract

We establish a necessary and sufficient condition for f ∈ H p ( R ) , g ∈ H q ( R ) with p −1 + q −1 ⩽ 1 to satisfy the Bedrosian identity H ( f g ) = f H g , where H denotes the Hilbert transform. As applications, we prove the Bedrosian theorem for this identity, and give a characterization of f satisfying the identity when g is a finite linear combination of complex sinusoids. We also show that if f is of low Fourier frequency then it is necessary for g to have high Fourier frequency in order to satisfy the Bedrosian identity.