Square roots of perturbed subelliptic operators on Lie groups

Details Square roots of perturbed subelliptic operators on Lie groups Square roots of perturbed subelliptic operators on Lie groups

2012-04-23

arxiv.org/abs/1204.5236v1

Mathematics

Analysis of PDEs

Scientific paper

We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower order terms. In this general setting we deduce inhomogeneous estimates. In case the group is nilpotent and the subelliptic operator is pure second order, then we prove stronger homogeneous estimates. Furthermore, we prove Lipschitz stability of the estimates under small perturbations of the coefficients.

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