Let $L$ be a homogeneous sublaplacian on the $6$-dimensional free $2$-step nilpotent Lie group $N_{3,2}$ on three generators. We prove a theorem of Mikhlin–Hörmander type for the functional calculus of $L$, where the order of differentiability $s > 6/2$ is required on the multiplier.
Keywords:
homogeneous sublaplacian dimensional step nilpotent lie group three generators prove theorem mikhlin rmander type functional calculus where order differentiability required multiplier
Affiliations des auteurs :
Alessio Martini
1
;
Detlef Müller
1
1
Mathematisches Seminar C.-A.-Universität zu Kiel Ludewig-Meyn-Str. 4 D-24118 Kiel, Germany
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author = {Alessio Martini and Detlef M\"uller},
title = {$L^p$ spectral multipliers on the free group $N_{3,2}$},
journal = {Studia Mathematica},
pages = {41--55},
year = {2013},
volume = {217},
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doi = {10.4064/sm217-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm217-1-3/}
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Alessio Martini; Detlef Müller. $L^p$ spectral multipliers on the free group $N_{3,2}$. Studia Mathematica, Tome 217 (2013) no. 1, pp. 41-55. doi: 10.4064/sm217-1-3
