## The Littlewood-Paley-Stein inequality for diffusion processes on general metric spaces

J. Math. Sci. Univ. Tokyo
Vol. 14 (2007), No. 1, Page 1--30.

KAWABI, Hiroshi ; MIYOKAWA, Tomohiro
The Littlewood-Paley-Stein inequality for diffusion processes on general metric spaces
In this paper, we establish the Littlewood-Paley-Stein inequality on general metric spaces %We show this inequality under a weaker condition than the lower boundedness of Bakry-Emery's $\Gamma_{2}$. We also discuss Riesz transforms. %a relationship of Sobolev norms. As examples, we deal with diffusion processes on a path space associated with stochastic partial differential equations (SPDEs in short) and a class of superprocesses with immigration.