Convolution operators of weak type (𝑝,𝑝) which are not of strong type (𝑝,𝑝)

Szwarc, Ryszard

doi:10.1090/S0002-9939-1983-0706538-1

Convolution operators of weak type $(p, p)$ which are not of strong type $(p, p)$
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Proc. Amer. Math. Soc. 89 (1983), 184-185 Request permission

Abstract:

We give an example of a locally compact group $G$ for which, for every $p$ with $2 < p < \infty$, there exists an operator of weak type $(p,p)$ commuting with the right translations on $G$ which is not of strong type $(p,p)$. This gives a negative solution of E. M. Stein’s problem.

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