On the failure of the Hörmander multiplier theorem in a limiting case (1805.09907v1)

Abstract: 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 $|1/p-1/2|=s/n$.