## 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
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Abstract:
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.

Keywords: Littlewood-Paley-Stein inequality, gradient estimate condition, Riesz transforms, SPDEs, superprocesses.

Mathematics Subject Classification (2000): 42B25, 60J60, 60H15.
Mathematical Reviews Number: MR2320383