On restricted weak type (1,1): The continuous case

Hagelstein, Paul; Jones, Roger

doi:10.1090/S0002-9939-04-07530-6

On restricted weak type $(1,1)$: The continuous case
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by Paul A. Hagelstein and Roger L. Jones PDF

Proc. Amer. Math. Soc. 133 (2005), 185-190 Request permission

Abstract:

Let $\mathbb {T}$ denote the unit circle. An example of a sublinear translation-invariant operator $T$ acting on $L^{1}\left (\mathbb {T}\right )$ is given such that $T$ is of restricted weak type $(1,1)$ but not of weak type $(1,1)$.

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