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

2018/05/24 by Slavíková, Lenka
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.09907

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.

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