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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Most Riesz product measures are $ L\sp p$-improving


Author: David L. Ritter
Journal: Proc. Amer. Math. Soc. 97 (1986), 291-295
MSC: Primary 43A15; Secondary 43A25
MathSciNet review: 835883
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Abstract: A Borel measure $ \mu $ on a compact abelian group $ G$ is $ {L^p}$-improving if, given $ p > 1$, there is a $ q = q(p,\mu ) > p$ and $ {\text{a}}\;K = K(p,q,\mu ) > 0$ such that $ {\left\Vert {\mu * f} \right\Vert _q} \leq K{\left\Vert f \right\Vert _p}$ for each $ f$ in $ {L^p}(G)$. Here the $ {L^p}$-improving Riesz product measures on infinite compact abelian groups are characterized by means of their Fourier transforms.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0835883-7
PII: S 0002-9939(1986)0835883-7
Article copyright: © Copyright 1986 American Mathematical Society