Decay of matrix coefficients on reductive homogeneous spaces of   spherical type
  Let Z be a homogeneous space Z=G/H of a real reductive Lie group G with a reductive subgroup H. The investigation concerns the quantitative decay of matrix coefficients on $Z$ under the assumption that Z is of spherical type, that is, minimal parabolic subgroups have open orbits on Z. 
Bernhard Kr\"otz, Eitan Sayag and Henrik Schlichtkrull
math.RT