Best constants in the vector-valued Littlewood-Paley-Stein theory

Guixiang Hong, Zhendong Xu, Hao Zhang

Let $L$ be a sectorial operator of type $\alpha$ ($0\le \alpha <\pi /2$) on $L^2({\mathbb{R}}^d)$ with the kernels of $\{e^{-tL}{\}}_{t>0}$ satisfying certain size and regularity conditions. Defi…