Decay of matrix coefficients on reductive homogeneous spaces of spherical type
Let $$Z$$Z be a homogeneous space $$Z=G/H$$Z=G/H of a real reductive Lie group $$G$$G with a reductive subgroup $$H$$H. The investigation concerns the quantitative decay of matrix coefficients on $$Z$$Z under the assumption that $$Z$$Z is of spherical type, that is, minimal parabolic subgroups have open orbits on $$Z$$Z.