A characterization of 𝐿^{𝑝}-improving measures

Hare, Kathryn E.

doi:10.1090/S0002-9939-1988-0920989-6

A characterization of $L^p$-improving measures
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Proc. Amer. Math. Soc. 102 (1988), 295-299 Request permission

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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Convolution by a biased coin

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