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arXiv · 1909.06879

Free Fourier Multipliers associated with the firstSegment

Tao Mei·Quanhua Xu
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Abstract

We study Fourier multipliers on free group $\mathbb{F}_\infty$ associated with the first segment of the reduced words, and prove that they are completely bounded on the noncommutative $L^p$ spaces $L^p(\hat{\mathbb{F}}_\infty)$ iff their restriction on $L^p(\hat{\mathbb{F}}_1)=L^p(\mathbb{T})$ are completely bounded. As a consequence, every classical Mikhlin multiplier extends to a $L^p$ Fourier multiplier on free groups for all $1<p<\infty$.

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Tao Mei, Quanhua Xu. 2019-09-15. Free Fourier Multipliers associated with the firstSegment. https://arxiv.org/abs/1909.06879

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