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, we prove stronger homogeneous estimates. Furthermore, we prove Lipschitz stability of the estimates under small perturbations of the coefficients.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-3-1,
author = {Lashi Bandara and A. F. M. ter Elst and Alan McIntosh},
title = {Square roots of perturbed subelliptic operators on Lie groups},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {193-217},
zbl = {1291.35036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-3-1}
}
Lashi Bandara; A. F. M. ter Elst; Alan McIntosh. Square roots of perturbed subelliptic operators on Lie groups. Studia Mathematica, Tome 215 (2013) pp. 193-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-3-1/