The Littlewood-Paley-Stein inequality for Dirichlet space tamed by signed measured curvature lower bounds

The notion of tamed Dirichlet space by distributional lower Ricci curvature bounds was proposed by Erbar–Rigoni–Sturm–Tamanini as the Dirichlet space having a weak form of Bakry–Émery curvature lower bounds in distribution sense. In this framework, we establish the Littlewood–Paley–Stein inequality for $L^p$-functions which partially generalizes the result by Kawabi–Miyokawa.