2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63067We prove $L^p$ estimates for the Walsh model of the maximal bi-Carleson operator (which is a hybrid of the bilinear Hilbert transform and the Carleson maximal operator which appears naturally in the eigenfunction problem for one-dimensional Schrodinger operators). The corresponding estimates for the Fourier model will be obtained in the sequel of this paper.36 pages, no figuresClassical Analysis and ODEs42B25; 42B20text