Characterizations of Besov and Triebel-Lizorkin Spaces on Metric Measure   Spaces
  On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel-Lizorkin spaces, including a pointwise characterization. Moreover, we discuss their (non)triviality under a Poincar\'e inequality. 
Amiran Gogatishvili, Pekka Koskela and Yuan Zhou
math.CA math.FA