Is there any relation between the values of surface fractal dimension Ds and the mass fractal dimension Dm for the mass fractal material especially for Dm < 2.
The short answer to this question is yes. The long answer can be found in Sec. 4.3 ('Potential theoretic methods') of the book Fractal Geometry, 2nd edition, by K Falconer (Wiley, Chichester, England, 2003). Note that here the mass distribution m(x) is related to the measure function μ(x) according to m(x) = dμ(x)/dx. More precisely, the mass content M(E) of the set E is equal to ∫E dμ(x). □