2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99273We characterize joint k-hyponormality for 2-variable weighted shifts. Using this characterization we construct a family of examples which establishes and illustrates the gap between k-hyponormality and (k+1)-hyponormality for each k>=1. As a consequence, we obtain an abstract solution to the Lifting Problem for Commuting Subnormals.13 pages; to appear in J. Funct. AnalFunctional Analysis47B20, 47B37, 47A13, 28A50text