Volume growth, temperedness and integrability of matrix coefficients on a real spherical space

Friedrich Knop, Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull

Published 2014-07-30, updated 2016-04-06Version 2

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.