Analysis of joint spectral multipliers on Lie groups of polynomial growth

Alessio Martini[1]

  • [1] Scuola Normale Superiore Piazza dei Cavalieri, 7 56126 Pisa (Italy)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 4, page 1215-1263
  • ISSN: 0373-0956

Abstract

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We study the problem of L p -boundedness ( 1 < p < ∞ ) of operators of the form m ( L 1 , ⋯ , L n ) for a commuting system of self-adjoint left-invariant differential operators L 1 , ⋯ , L n on a Lie group G of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when G is a homogeneous group and L 1 , ⋯ , L n are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.

How to cite

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Martini, Alessio. "Analysis of joint spectral multipliers on Lie groups of polynomial growth." Annales de l’institut Fourier 62.4 (2012): 1215-1263. <http://eudml.org/doc/251125>.

@article{Martini2012,
abstract = {We study the problem of $L^p$-boundedness ($1 &lt; p &lt; \infty $) of operators of the form $m(L_1,\dots ,L_n)$ for a commuting system of self-adjoint left-invariant differential operators $L_1,\dots ,L_n$ on a Lie group $G$ of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when $G$ is a homogeneous group and $L_1,\dots ,L_n$ are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.},
affiliation = {Scuola Normale Superiore Piazza dei Cavalieri, 7 56126 Pisa (Italy)},
author = {Martini, Alessio},
journal = {Annales de l’institut Fourier},
keywords = {spectral multipliers; joint functional calculus; differential operators; Lie groups; polynomial growth; singular integral operators},
language = {eng},
number = {4},
pages = {1215-1263},
publisher = {Association des Annales de l’institut Fourier},
title = {Analysis of joint spectral multipliers on Lie groups of polynomial growth},
url = {http://eudml.org/doc/251125},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Martini, Alessio
TI - Analysis of joint spectral multipliers on Lie groups of polynomial growth
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 4
SP - 1215
EP - 1263
AB - We study the problem of $L^p$-boundedness ($1 &lt; p &lt; \infty $) of operators of the form $m(L_1,\dots ,L_n)$ for a commuting system of self-adjoint left-invariant differential operators $L_1,\dots ,L_n$ on a Lie group $G$ of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when $G$ is a homogeneous group and $L_1,\dots ,L_n$ are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.
LA - eng
KW - spectral multipliers; joint functional calculus; differential operators; Lie groups; polynomial growth; singular integral operators
UR - http://eudml.org/doc/251125
ER -

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