Abstract:
We obtain necessary conditions for a bounded
function $\varphi$ to be a Fourier multiplier of weak type
$\bigl(\psi(L)(G),\psi(L)(G)\bigr)$, where $G=\mathbb R^d$
or $G=\mathbb T^d$, provided that the Young function $\psi(t)$
grows slower than $t\ln^{1/2}t$ as $t$ tends to infinity.
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