Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free Fourier Multipliers associated with the firstSegment   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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The categories of this paper are: q-bio
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph