Vol. 63, No. 2, 1976

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Sets of uniqueness and multiplicity for Lp

Anna Maria Mantero

Vol. 63 (1976), No. 2, 467–480
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 Lq(Γ) and, at the same time, a set of multiplicity for Lp(Γ).

This is followed by some results of the same type concerning the spaces Lp,α(Γ), α0, when G is the Cantor group.

Mathematical Subject Classification 2000
Primary: 43A15
Secondary: 42A48
Milestones
Received: 5 April 1972
Published: 1 April 1976
Authors
Anna Maria Mantero