Multipliers of 𝐿^{𝑝}_{𝐸}. I

Oberlin, Daniel M.

doi:10.1090/S0002-9947-1976-0402417-9

Multipliers of $L^ p_ E$. I
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by Daniel M. Oberlin

Trans. Amer. Math. Soc. 221 (1976), 187-198

DOI: https://doi.org/10.1090/S0002-9947-1976-0402417-9

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Abstract:

Let X be an abelian group, the character group of a compact group G. For a subset E of X let $L_E^p$ be the subspace of E-spectral functions in ${L^p}(G)$. We show that if X is infinite and $1 \leqslant p < 2$, then E can be chosen so that not every multiplier of $\widehat {L_E^p}$ extends to a multiplier of $\widehat {{L^p}}(G)$.

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