Geodesic
Square roots of perturbed subelliptic operators on Lie groups
Lashi Bandara 1   ; A. F. M. ter Elst 2   ; Alan McIntosh 1
1 Centre for Mathematics and its Applications Mathematical Sciences Institute Australian National University Canberra, ACT 0200, Australia
2 Department of Mathematics University of Auckland Private bag 92019 Auckland 1142, New Zealand
Studia Mathematica, Tome 216 (2013) no. 3, pp. 193-217 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm216-3-1
Keywords: solve kato square root problem bounded measurable perturbations subelliptic operators connected lie groups subelliptic operators divergence form operators complex bounded coefficients which may have lower order terms general setting deduce inhomogeneous estimates group nilpotent subelliptic operator pure second order prove stronger homogeneous estimates furthermore prove lipschitz stability estimates under small perturbations coefficients

Lashi Bandara  1   ; A. F. M. ter Elst  2   ; Alan McIntosh  1

1 Centre for Mathematics and its Applications Mathematical Sciences Institute Australian National University Canberra, ACT 0200, Australia
2 Department of Mathematics University of Auckland Private bag 92019 Auckland 1142, New Zealand 
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Lashi Bandara; A. F. M. ter Elst; Alan McIntosh. Square roots of perturbed subelliptic
 operators on Lie groups. Studia Mathematica, Tome 216 (2013) no. 3, pp. 193-217. doi: 10.4064/sm216-3-1

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