We consider a family of non-unimodular rank one NA-groups with roots not all positive, and we show that on these groups there exists a distinguished left invariant sub-Laplacian which admits a differentiable functional calculus for every p ≥ 1.
For any two continuous maps , between two solvmanifolds of the same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of , . This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.
Let be a nilpotent Lie algebra which is also regarded as a homogeneous Lie group with the Campbell-Hausdorff multiplication. This allows us to define a generalized multiplication of two functions in the Schwartz class (*), where and are the Abelian Fourier transforms on the Lie algebra and on the dual * and ∗ is the convolution on the group . In the operator analysis on nilpotent Lie groups an important notion is the one of symbolic calculus which can be viewed as a higher order generalization...
We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.