Localization operators on homogeneous spaces

Let G be a locally compact group, H a compact subgroup of G and $ a representation of the homogeneous space G/H on a Hilbert space H. For ψ ∈ L p (G/H), 1 ≤ p ≤ ∞, and an admissible wavelet ζ for $, we define the localization operator Lψ,ζ on H and we show that it is a bounded operator. Moreover, we prove that the localization operator is in Schatten p-class and it ≤ ∞ 1 ≤ p is a compact operator for