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.

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.
2021
Biagi S.; Bonfiglioli A.; Bramanti M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/816788
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