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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of $ L^p$-improving measures


Author: Kathryn E. Hare
Journal: Proc. Amer. Math. Soc. 102 (1988), 295-299
MSC: Primary 43A22,; Secondary 42A45,42A85
MathSciNet review: 920989
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Abstract: A Borel measure $ \mu $ on a compact abelian group $ G$ is $ {L^p}$-improving if $ \mu $ convolves $ {L^p}(G)$ to $ {L^{p + \varepsilon }}(G)$ for some $ \varepsilon > 0$. We characterize $ {L^p}$-improving measures by means of their Fourier transforms.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0920989-6
Keywords: $ {L^p}$-improving measure, $ \Lambda (p)$ set
Article copyright: © Copyright 1988 American Mathematical Society