On the failure of the H\"ormander multiplier theorem in a limiting case

Lenka Slavíková

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arXiv · 1805.09907

On the failure of the H\"ormander multiplier theorem in a limiting case

Lenka Slavíková

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

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Lenka Slavíková. 2018-05-24. On the failure of the H\"ormander multiplier theorem in a limiting case. https://arxiv.org/abs/1805.09907

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