Inserted: 13 sep 2013
Last Updated: 19 dec 2014
Journal: Journal of Geometric Analysis
We prove higher summability and regularity of $\Gamma(f)$ for functions $f$ in spaces satisfying the Bakry-Èmery condition $BE(K,\infty)$.
As a byproduct, we obtain various equivalent weak formulations of $BE(K,N)$ and we prove the Local-to-Global property of the $RCD^*(K,N)$ condition in locally compact metric measure spaces $(X,d,m)$, without assuming a priori the non-branching condition on the metric space.