On the Bakry-Émery condition, the gradient estimates and the Local-to-Global property of RCD∗(K,N) metric measure spaces
نویسندگان
چکیده
We prove higher summability and regularity of Γ ( f ) for functions f in spaces satisfying the Bakry-Émery condition BE(K,∞). 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.
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