Some equivalent definitions of high order Sobolev spaces on stratified groups and generalizations to metric spaces

By Yong-ping Liu, G. Lu, R. Wheeden. 2002

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New characterizations of Hajłasz-Sobolev spaces on metric spaces (2003, background): “[6, 10 ], in this paper, we study the fractional versions of the Haj�lasz-Sobolev spaces on the space of homogeneous type in the sense of Coifman and Weiss [11] .”
A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces (2009, background): “Since Hajłasz in [13] introduced Sobolev spaces on any metric measure space, a series of papers has been devoted to the construction and investigation of Sobolev spaces of various types on metric measure spaces; see, for example, [15, 30, 8, 10, 31, 42, 20, 21, 28, 5, 14, 9, 49].”
Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below (2014, methodology): “To the best of our knowledge, attempts to define higher order Sobolev spaces on metric measure spaces have been done only in [39] and [1].”