2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144392In this paper, we initiate the study of sub-pluriharmonic curves in Cuntz-Toeplitz algebras and free pluriharmonic majorants on noncommutative balls. We are lead to a characterization of the noncommutative Hardy space $H^2_{\bf ball}$ in terms of free pluriharmonic majorants, and to a Schur type description of the unit ball of $H^2_{\bf ball}$. These results are used to solve a multivariable commutant lifting problem and provide a description of all solutions.35 pagesFunctional AnalysisOperator Algebras47A57; 47A20; 47A56; 46L52text