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

Abstract

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.