  Let E be a compact set in the plane, g be a K-quasiconformal map, and let
0<t<2. Then
  H^t (E) = 0 implies H^{t'} (g E) = 0, for t'=[2Kt]/[2+(K-1)t].
  This is a refinement of a set of inequalities on the distortion of Hausdorff
dimensions by quasiconformal maps proved by K. Astala in his celebrated paper
on area distortion for quasiconformal maps and answers in the positive a
Conjecture of K. Astala in op. cit.
