Analysis of joint spectral multipliers on Lie groups of polynomial growth

Abstract

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-Hörmander and Marcinkiewicz multiplier theorems.

37 pages

References in corpus (3)

• Algebras of differential operators on Lie groups and spectral multipliers
• Spectral theory for commutative algebras of differential operators on Lie groups
• Gelfand transforms of SO(3)-invariant Schwartz functions on the free group N_{3,2}

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