Following [1] we define the bilinear Hilbert transform of ultradistributions H_{\alpha}^{*} : {\cal D}^{\prime} (*, L^{2}) \times {\cal D} (*, L^{\infty}) \rightarrow {\cal D}^{\prime} (*, L^{2}) , respectively H_{\alpha}^{*}{:}\ {\cal D}^{\prime} (*, L^{q_{1}}) \times {\cal D} (*, L^{p_{2}}) \rightarrow {\cal D}^{\prime} (*, L^{q}) , where {\cal D}^{\prime} (*, L^{2}) , and {\cal D}^{\prime} (*, L^{q}) , are subspaces of the space of Beurling (Roumieu) ultradistributions {\cal D}^{\prime} (*) = {\cal D}^{\prime} (*, R^{n}) ( * is a common notation for Beurling and Roumieu type spaces). We give the inversion formula and discuss the general bilinear Hilbert transform of ultradistributions. Also, the product of ultradistributions is connected with this transformation.
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