Temperedness of reductive homogeneous spaces
  Let G be a semisimple algebraic Lie group and H a reductive subgroup. We find geometrically the best even integer p for which the representation of G in L^2(G/H) is almost L^{p}. As an application, we give a criterion which detects whether this representation is tempered. 
Yves Benoist and Toshiyuki Kobayashi
math.RT math.FA