Most Riesz Product Measures are Lp-Improving

Most Riesz Product Measures are Lp-Improving

A Borel measure μ on a compact abelian group G is Lp-improving if, given$p > 1$, there is a$q = q(p, \mu) > p$and a$K = K(p, q, \mu) > 0$such that |μ* f|q≤ K|f|pfor each f in Lp(G). Here the Lp-improving Riesz product measures on infinite compact abelian groups are characterized by means of...

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Veröffentlicht in:Proceedings of the American Mathematical Society 1986-06, Vol.97 (2), p.291-295
1. Verfasser: Ritter, David L.
Format: Artikel
Sprache:eng
Schlagworte:
Borel measures
Fourier transformations
Haar measures
Harmonic analysis
Mathematical theorems
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Zusammenfassung:A Borel measure μ on a compact abelian group G is Lp-improving if, given$p > 1$, there is a$q = q(p, \mu) > p$and a$K = K(p, q, \mu) > 0$such that |μ* f|q≤ K|f|pfor each f in Lp(G). Here the Lp-improving Riesz product measures on infinite compact abelian groups are characterized by means of their Fourier transforms.
ISSN:0002-9939
1088-6826
DOI:10.2307/2046516