2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209662We study tent spaces on general measure spaces $(Ω, μ)$. We assume that there exists a semigroup of positive operators on $L^p(Ω, μ)$ satisfying a monotone property but do not assume any geometric/metric structure on $Ω$. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman's $H^1$-BMO duality theory. We also get a $H^1$-BMO duality inequality without assuming the monotone property. All the results are proved in a more general setting, namely for noncommutative $L^p$ spaces.The statement of Lemma 3.11 is correctedFunctional AnalysisClassical Analysis and ODEs46L52 (Primary); 32C05 (Secondary)text