2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68759In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foias, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative commutant lifting theorem. This is used to solve new operator-valued interpolation problems of Schur-Caratheodory, Nevanlinna-Pick, and Sarason type on Fock spaces. Some consequences to norm constrained analytic interpolation in the unit ball of C^n are also considered.19 pagesFunctional AnalysisOperator Algebras47A57, 47A63 (Primary) 47A56, 47A20, 47B47 (Secondary)text