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,a}(Γ), a ≠ 0, when G is the Cantor group.
Sets of uniqueness and multiplicity for L^p
MANTERO, ANNA MARIA
1976-01-01
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,a}(Γ), a ≠ 0, when G is the Cantor group.
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