ANALYSIS OF JOINT SPECTRAL MULTIPLIERS ON LIE GROUPS OF POLYNOMIAL GROWTH

We study the problem of L-p-boundedness (1 < p < infinity) 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-Hormander and Marcinkiewicz multiplier theorems.