From the Littlewood-Paley-Stein Inequality to the Burkholder-Gundy Inequality

Zhendong Xu, Hao Zhang

Let $\{{\mathsf{T}}_t{\}}_{t>0}$ be a symmetric diffusion semigroup on a $\sigma$-finite measure space $(\Omega ,\mathcal{A},\mu )$ and $G^{\mathsf{T}}$ the associated Littlewood-Paley $g$-functio…