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

Abstract

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.

Additional material of 4 pages added. To appear in J. Funct. Analysis

References in corpus (2)

• Simple compactifications and polar decomposition of homogeneous real spherical spaces
• The local structure theorem for real spherical varieties

Cited by in corpus (4)

• Classification of reductive real spherical pairs II. The semisimple case
• Classification of reductive real spherical pairs I. The simple case
• Plancherel theory for real spherical spaces: Construction of the Bernstein morphisms
• The tempered spectrum of a real spherical space