Analysis of joint spectral multipliers on Lie groups of polynomial growth
Abstract
We study the problem of Lp-boundedness (1 < p < ∞) of operators of the form m(L1,...,Ln) for a commuting system of self-adjoint left-invariant differential operators L1,...,Ln 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 L1,...,Ln are homogeneous, we prove analogues of the Mihlin-H\"ormander and Marcinkiewicz multiplier theorems.
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