Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Etude de deux classes de groupes nilpotents de pas deux   The aim of my PhD work is to study the $L^p$-boundedness of operators on two
classes of two-step nilpotent Lie groups, using Plancherel formulas and
spherical functions as tools. The first class of groups consists of the groups
of Heisenberg type, and the second, of the two-step free nilpotent Lie groups
(denoted $N_{v,2}$ for $v$ generators). In the latter case, we develop a radial
Fourier calculus. Our study has focused on the maximal functions associated
with Kor\'anyi spheres, together with their square functions, and the
convolution operator defined with the radial Fourier calculus on the two-step
free nilpotent Lie group (radial Fourier multipliers problem). In fact, one
chapter of this work is devoted to the proof of $L^p$-inequalities for the
maximal spherical function on the two considered classes of groups. Our method
is based on interpolation for the same operator family as in the euclidean
case, on $L^p$-boundedness for the standard maximal function, and
$L^2$-inequalities for square functions. These $L^2$-inequalities are based on
Plancherel formula and on the properties of bounded spherical functions for the
orthogonal group. On $N_{v,2}$, we construct the bounded spherical functions
using representations of the semidirect product of $N_{v,2}$ with the
orthogonal group. We also obtain some properties of the Kohn sublaplacian and
the radial Plancherel measure. Then we present a first study of the radial
Fourier multiplier problem, with the aim of giving our solutions for some
technicals difficulties.

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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn