Let L=∑j=1mXj2 be a Hörmander sum of squares of vector fields in space Rn, where any Xj is homogeneous of degree 1 with respect to a family of non-isotropic dilations in space. In this paper we prove global estimates and regularity properties for L in the X-Sobolev spaces WXk,p(Rn), where X={X1,…,Xm}. In our approach, we combine local results for general Hörmander sums of squares, the homogeneity property of the Xj's, plus a global lifting technique for homogeneous vector fields.
Biagi, S., Bonfiglioli, A., Bramanti, M. (2021). Global estimates in Sobolev spaces for homogeneous Hörmander sums of squares. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 498(1), 1-19 [10.1016/j.jmaa.2021.124935].
Global estimates in Sobolev spaces for homogeneous Hörmander sums of squares
Biagi S.;Bonfiglioli A.
;Bramanti M.
2021
Abstract
Let L=∑j=1mXj2 be a Hörmander sum of squares of vector fields in space Rn, where any Xj is homogeneous of degree 1 with respect to a family of non-isotropic dilations in space. In this paper we prove global estimates and regularity properties for L in the X-Sobolev spaces WXk,p(Rn), where X={X1,…,Xm}. In our approach, we combine local results for general Hörmander sums of squares, the homogeneity property of the Xj's, plus a global lifting technique for homogeneous vector fields.| File | Dimensione | Formato | |
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