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

Lenka Slavíková

doi:10.4171/rmi/1157

JournalsrmiVol. 36, No. 4pp. 1013–1020

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

Lenka Slavíková
University of Missouri, Columbia, USA and Charles University, Prague, Czechia

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Abstract

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 $∣1/ p - 1/2∣ = s / n$ .

Cite this article

Lenka Slavíková, On the failure of the Hörmander multiplier theorem in a limiting case. Rev. Mat. Iberoam. 36 (2020), no. 4, pp. 1013–1020

DOI 10.4171/RMI/1157