  We present various results on the equivalence and mapping properties under
affine transformations of fractional-order Sobolev norms and semi-norms of
orders between zero and one. Main results are mutual estimates of the three
semi-norms of Sobolev-Slobodeckij, interpolation and quotient space types. In
particular, we show that the former two are uniformly equivalent under affine
mappings that ensure shape regularity of the domains under consideration.
