Convolution operators of weak type (2,2) which are not of strong type (2,2)

Szwarc, Ryszard

doi:10.1090/S0002-9939-1983-0687644-7

Convolution operators of weak type $(2, 2)$ which are not of strong type $(2, 2)$
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Proc. Amer. Math. Soc. 87 (1983), 695-698 Request permission

Abstract:

It is well known that if $G$ is a locally compact and amenable group then the Banach spaces of operators of weak type $(2,2)$ and of strong type $(2,2)$ commuting with the right translations on $G$ are the same. In contrast we show that if $G$ is a nonabelian free group then there exists an operator of weak type $(2,2)$ commuting with the right translations on $G$ which is not of strong type $(2,2)$.

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