Geodesic
On necessary conditions for Fourier multipliers of weak type
Izvestiya. Mathematics , Tome 71 (2007) no. 1, pp. 75-95

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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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     author = {A. V. Rozhdestvenskii},
     title = {On necessary conditions for {Fourier} multipliers of weak type},
     journal = {Izvestiya. Mathematics },
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2007_71_1_a5/}
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A. V. Rozhdestvenskii. On necessary conditions for Fourier multipliers of weak type. Izvestiya. Mathematics , Tome 71 (2007) no. 1, pp. 75-95. http://geodesic.mathdoc.fr/item/IM2_2007_71_1_a5/