S p Norm Inequalities, 1 ≤ p ≤ ∞

Abstract

We prove in this chapter that a localization operator L F,φ : X → X associated to a function F in L p (G), 1 ≤ p ≤ ∞, and an admissible wavelet φ for an irreducible and square-integrable representation of a locally compact and Hausdorff group G on a Hilbert space X is in the Schatten-von Neumann class S p , 1 ≤ p ≤ ∞. When p = 1, the irreducibility of the representation π: G → U(X) can be dispensed with.