On the failure of the Hormander multiplier theorem in a limiting case

Abstract

We discuss the Hormander 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 vertical bar 1/p-1/2 vertical bar = s/n.

Keywords

• Hormander multiplier theorem
• Sobolev space