Sets of uniqueness and multiplicity for L^p

Anna Maria Mantero

Vol. 63 (1976), No. 2, 467–480

DOI: 10.2140/pjm.1976.63.467

Abstract

In the first part of this paper, it is proved that: if 1 < q < p ≦ 2 and G is a nondiscrete, locally compact abelian (LCA) group with character group Γ, there exists a subset of positive measure E ⊂ G which is a set of uniqueness for L^q(Γ) and, at the same time, a set of multiplicity for L^p(Γ).

This is followed by some results of the same type concerning the spaces L^p,α(Γ), α≠0, when G is the Cantor group.

Mathematical Subject Classification 2000

Primary: 43A15

Secondary: 42A48

Milestones

Received: 5 April 1972

Published: 1 April 1976