ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 43 42 26 Grinnell, Raymond, University of the West Indies, Barbados Two real functions associated with convolutions of measures Let M denote the set of Borel measures on an infinite compact abelian group. For μ ∈ M, the indexfunction is defined by I(μ, p) = sup{q ≥ p | μ ∗ L^{p} ⊆ L^{q}} where p ∈ [1, ∞). For a fixed p ∈ [1, ∞), the measurefunction I(·, p) is defined on M by I(μ, ·). Real-variable properties and examples of these two functions are discussed.