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

TL;DR

This paper proves a Littlewood-Paley-Stein inequality for Dirichlet spaces with distributional Ricci curvature bounds, extending previous results to a more general curvature-tamed setting.

Contribution

It establishes the Littlewood-Paley-Stein inequality for tamed Dirichlet spaces with distributional Ricci curvature bounds, generalizing earlier work by Kawabi and Miyokawa.

Findings

Proved Littlewood-Paley-Stein inequality in this new setting

Extended previous inequalities to distributional curvature bounds

Enhanced understanding of analysis on curvature-tamed Dirichlet spaces

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--\'Emery 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.