The Bedrosian Identity for Lp Function and the Hardy Space on Tube

Abstract

In this paper, we are devoted to establishing several necessary and su cient conditions for f∈Lp(Rn); g∈Lq(Rn) with (1/p) +(1/q)≤1 to satisfy the Bedrosian identity H(fg) =fHg, where H denotes the n-dimensional Hilbert transform. In addition, we also show that the distribution f∈DLp' (Rn) can be represented by functions in the Hardy space on tube.

Keywords

• Bedrosian identity|Fourier transform|Hilbert transform|Distribution