On a trilinear form related to the Carleson theorem

Demeter and Thiele introduced the two-dimensional bilinear Hilbert transform in Demeter and Thiele (2010) [3] and showed that the Carleson operator can be identified in particular instances of the corresponding trilinear form. Demeter considered the Walsh model of one such form in Demeter (2012) [2], in relation to the discussion of the Walsh–Carleson theorem. We prove boundedness of this trilinear form for a single triple of exponents at the boundary of the previously established range. For this purpose, we adapt the multilinear Bellman function technique from Kovač (2011) [5] to the one-and-a-half-dimensional time–frequency space.