| Abstract: | Abstract A measure μ on a compact group is called Lorentz-improving if for some 1 > p > ∞ and 1 → q 1 > q 2 ∞ μ *L (p, q 2) ? L(p, q 1). Let T μ denote the operator on L 2 defined by T μ(f) = μ * f. Lorentz-improving measures are characterized in terms of the eigenspaces of T μ, if T μ is a normal operator, and in terms of the eigenspaces of |T μ| otherwise. This result generalizes our recent characterization of Lorentz-improving measures on compact abelian groups and is modelled after Hare's characterization of L p -improving measures on compact groups. |
