Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth Fourier multipliers in group algebras via Sobolev dimension   We investigate Fourier multipliers with smooth symbols defined over locally
compact Hausdorff groups. Our main results in this paper establish new
H\"ormander-Mikhlin criteria for spectral and non-spectral multipliers. The key
novelties which shape our approach are three. First, we control a broad class
of Fourier multipliers by certain maximal operators in noncommutative $L_p$
spaces. This general principle ---exploited in Euclidean harmonic analysis
during the last 40 years--- is of independent interest and might admit further
applications. Second, we replace the formerly used cocycle dimension by the
Sobolev dimension. This is based on a noncommutative form of the Sobolev
embedding theory for Markov semigroups initiated by Varopoulos, and yields more
flexibility to measure the smoothness of the symbol. Third, we introduce a dual
notion of polynomial growth to further exploit our maximal principle for
non-spectral Fourier multipliers. The combination of these ingredients yields
new $L_p$ estimates for smooth Fourier multipliers in group algebras.

11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: stat