BILINEAR HILBERT TRANSFORM IN \(\mathcal{G}_{L^{p_1}} \times \mathcal{G}_{L^{p_2}}\)

Abstract

Bilinear Hilbert transform in appropriate Colombeau algebras \(\mathcal{G}_{L^{p_1}} \times \mathcal{G}_{L^{p_2}}\) are given. The relations of bilinear Hilbert transforms with the corresponding definitions in Colombeau algebras are given through special regularizations.