Differences of Vector-Valued Functions on Topological Groups

Differences of Vector-Valued Functions on Topological Groups

Let G be a locally compact group equipped with right Haar measure. The right differences Δhφof functions φ on G are defined by Δhφ(t) = φ(th) - φ(t) for h, t ∈ G. Let φ ∈ L∞(G) and suppose Δhφ∈ Lp(G) for some $1 \leq p < \infty$ and all h ∈ G. We prove that |Δhφ|pis a right uniformly continuous f...

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Veröffentlicht in:Proceedings of the American Mathematical Society. - American Mathematical Society, 1950. - 124(1996), 7, Seite 1969-1975
1. Verfasser: Basit, Bolis (VerfasserIn)
Weitere Verfasser: Pryde, A. J.
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1996
Zugriff auf das übergeordnete Werk:Proceedings of the American Mathematical Society
Schlagworte:Differences weight functions spectrum right uniform continuity G-modules weak continuity absolutely continuous elements Mathematics
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520 |a Let G be a locally compact group equipped with right Haar measure. The right differences Δhφof functions φ on G are defined by Δhφ(t) = φ(th) - φ(t) for h, t ∈ G. Let φ ∈ L∞(G) and suppose Δhφ∈ Lp(G) for some $1 \leq p < \infty$ and all h ∈ G. We prove that |Δhφ|pis a right uniformly continuous function of h. If G is abelian and the Beurling spectrum sp(φ) does not contain the unit of the dual group Ĝ, then we show φ ∈ Lp(G). These results have analogues for functions φ: G → X, where X is a separable or reflexive Banach space. Finally, we apply our methods to vector-valued right uniformly continuous differences and to absolutely continuous elements of left Banach G-modules. 
540 |a Copyright 1996 American Mathematical Society 
650 4 |a Differences 
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