Revista Matemática Iberoamericana


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Published online first: 2019-12-17
DOI: 10.4171/rmi/1157

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

Lenka Slavíková[1]

(1) University of Missouri, Columbia, USA and Charles University, Prague, Czechia

We discuss the Hörmander 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 $|1/p-1/2|=s/n$.

Keywords: Hörmander multiplier theorem, Sobolev space

Slavíková Lenka: On the failure of the Hörmander multiplier theorem in a limiting case. Rev. Mat. Iberoam. Electronically published on December 17, 2019. doi: 10.4171/rmi/1157 (to appear in print)