Non-doubling Ahlfors Measures, Perimeter Measures, And the Characterization of the Trace Spaces of Sobolev Functions in Carnot-caratheodory Spaces

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Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups (2009, background): “It continues our program in this area [5, 4, 7], which is one component in a worldwide endeavor investigating sub-Riemannian geometric measure theory, including theories of rectifiability and perimeter [14], [26], [27], [17], [42], [3], [39]; fractals and tilings [56], [57]; geometric analysis of no”
On traces of Sobolev functions on the boundary of extension domains (2009, background): “Note that for s := N − d an upper/lower d-Ahlfors measure on S is called an upper/lower s-Ahlfors measure in [7].”
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].”
Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces (2017, background): “For more information on fractional order Sobolev spaces we refer to [6, 8, 21, 30, 37, 50] and their references.”