Analysis of joint spectral multipliers on Lie groups of polynomial growth

Details Analysis of joint spectral multipliers on Lie groups of polynomial growth Analysis of joint spectral multipliers on Lie groups of polynomial growth

2010-10-06

arxiv.org/abs/1010.1186v2

Mathematics

Functional Analysis

37 pages

Scientific paper

We study the problem of L^p-boundedness (1 < p < \infty) 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-H\"ormander and Marcinkiewicz multiplier theorems.

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