乘积函数的双Hilbert变换和Bedrosian等式

The double Hilbert transform and the double Bedrosian identity of the product functions

本文研究双Hilbert变换的性质,并对于f∈L^p(R^2), g∈L^q(R^2), p^(-1)+q^(-1)≤1,探讨在双Hilbert变换作用下Bedrosian等式H_2H_1(fg)=fH_2H_1g成立的充要条件,其中H_2H_1是双Hilbert变换.

We give some properties of the double Hilbert transform, and then establish the necessary and sufficient conditions for f ∈ Lp（R2）, g ∈ Lq（R2）, p-1＋ q-1≤1 to satisfy the double Bedrosian identity H2H1（f g） = fH2H1g, where H2H1 denotes the double Hilbert transform.