On the failure of the H\"ormander multiplier theorem in a limiting case

We discuss the H"ormander multiplier theorem for $L^p$ boundedness of Fourier multipliers in which the multiplier belongs to a fractional Sobolev space with smoothness $s$. We show that this theorem does not hold in the limiting case $\mathrm{\mid }1\mathrm{/}p-1\mathrm{/}2\mathrm{\mid }=s\mathrm{/}n$.