Volume growth, temperedness and integrability of matrix coefficients on   a real spherical space
  We apply the local structure theorem and the polar decomposition to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure $L^p$-integrability of matrix coefficients on Z. 
Friedrich Knop, Bernhard Kr\"otz, Eitan Sayag, Henrik Schlichtkrull
math.RT